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Recent questions tagged differentiation


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Evaluate \(\frac{d}{d x} f(x)\) using the rules for differentiation: \[ f(x)=-\frac{1}{2} x^{4}-2 x^{3}+\frac{1}{2} \sqrt{x^{5}} \]

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Find \(h^{\prime}(x)\) using the rules for differentiation: \[ h(x)=2 x^{2}+4 x-1 \]
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Given: \[ a=\frac{1}{2} y^{3}+5 y+2 \] Determine \(\frac{d}{d y} a\) using the rules for differentiation.

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Find \(D_{x} h(x)\) using the rules for differentiation: \[ h(x)=6 x^{4}-6 x^{3}-5 x^{2} \]
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Find \(\frac{d}{d x} f(x)\) using the rules for differentiation: \[ f(x)=-3 x^{2}-6 x+6 \]
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What are the rules of differentiation?
1 answer 5 views
What are the rules of differentiation?What are the rules of differentiation? ...
by MathsGee Platinum
(104,048 points)
asked in Mathematics Jan 15
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has
0 answers 4 views
The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has   A. no extremum, B. exactly one maximum, C. exactly one minimum, D. exactly ...
by MathsGee Platinum
(104,048 points)
asked in Mathematics Jan 13
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If \(\sin x+\cos x=\sqrt{y+\frac{1}{y}}, x \in[0, \pi]\), then:
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The number of \(x \in[0,2 \pi]\) for which \(\left|\sqrt{2 \sin ^{4} x+18 \cos ^{2} x}-\sqrt{2 \cos ^{4} x+18 \sin ^{2} x}\right|=1\) is:

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WHat is the formal definition of the derivative of a function \(f(x)\)?
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Write down the expansion of \((1+x)^{7}\) in ascending powers of \(x\).
1 answer 65 views
Write down the expansion of \((1+x)^{7}\) in ascending powers of \(x\).(a)(i) Write down the expansion of \((1+x)^{7}\) in ascending powers of \(x\). (ii) If the coefficients of the fifth, sixth and seventh terms in the e ...
by MathsGee Platinum
(104,048 points)
asked in Mathematics Sep 12, 2021
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Evaluate: \(\int_{1}^{3}\left(\frac{x-1}{(x+1)^{2}}\right) \mathrm{d} x\)
1 answer 46 views
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Evaluate \(\int_{-1}^{0}(x+1)(x-2) \mathrm{d} x\)
1 answer 22 views
Evaluate \(\int_{-1}^{0}(x+1)(x-2) \mathrm{d} x\)Evaluate \(\int_{-1}^{0}(x+1)(x-2) \mathrm{d} x\) A. \(\frac{7}{6}\) B. \(\frac{5}{6}\) C. \(\frac{-5}{6}\) D. \(\frac{-7}{6}\) ...
by Siyavula Bronze Status
(7,026 points)
asked in Mathematics Sep 11, 2021
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Find the coefficient of \(x^{4}\) in the expansion of \((1-2 x)^{6}\)
1 answer 55 views
Find the coefficient of \(x^{4}\) in the expansion of \((1-2 x)^{6}\)Find the coefficient of \(x^{4}\) in the expansion of \((1-2 x)^{6}\) A. \(-320\) B. \(-240\) C. 240 D. 320 ...
by Siyavula Bronze Status
(7,026 points)
asked in Mathematics Sep 11, 2021
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Evaluate \(\int \dfrac{1}{16+x^{2}} d x\)
1 answer 18 views
Evaluate \(\int \dfrac{1}{16+x^{2}} d x\)Evaluate \(\int \dfrac{1}{16+x^{2}} d x\) ...
by Siyavula Bronze Status
(7,026 points)
asked in Mathematics Sep 11, 2021
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Evaluate $\int \cos ^{3} x d x$
1 answer 27 views
Evaluate $\int \cos ^{3} x d x$Evaluate $\int \cos ^{3} x d x$ ...
by Siyavula Bronze Status
(7,026 points)
asked in Mathematics Sep 11, 2021
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Use differentiation to find \(\mathrm{f}^{\prime}(x)\).
1 answer 24 views
Use differentiation to find \(\mathrm{f}^{\prime}(x)\).\ f(x)=x^{3}-3 x^{2}+5 x-4 \ (a) Use differentiation to find \(\mathrm{f}^{\prime}(x)\). The equation \(\mathrm{f}(x)=0\) has a root \(\alpha\) in ...
by MathsGee Platinum
(104,048 points)
asked in Mathematics Sep 9, 2021
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Evaluate \(\int_{0}^{1} \dfrac{\ln x}{\sqrt{1+x^{4}}}\)
0 answers 42 views
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Determine \(f^{\prime}(x)\) if \(f(x)=-4 x^{2}\).
1 answer 34 views
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Determine \(f^{\prime}(x)\) if \(f(x)=7 x^{2}\).
1 answer 24 views
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Determine \(f^{\prime}(x)\) if \(f(x)=-2 x-2\).
1 answer 30 views
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Determine \(f^{\prime}(x)\) if \(f(x)=4 x+7\).
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Determine \(f^{\prime}(x)\) if \(f(x)=-7 x+7\).
1 answer 20 views
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Determine \(f^{\prime}(x)\) if \(f(x)=-1\).
1 answer 27 views
Determine \(f^{\prime}(x)\) if \(f(x)=-1\).Determine \(f^{\prime}(x)\) if \(f(x)=-1\). ...
by MathsGee Platinum
(104,048 points)
asked in Mathematics Aug 31, 2021
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