# arrow_back Evaluate $g^{\prime}(x)$ using the rules for differentiation: $g(x)=-\frac{1}{2} x^{\frac{7}{2}}+\frac{3}{4} \sqrt[4]{x^{3}}-\frac{4}{3} x^{\frac{1}{2}}$

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Evaluate $g^{\prime}(x)$ using the rules for differentiation:
$g(x)=-\frac{1}{2} x^{\frac{7}{2}}+\frac{3}{4} \sqrt[4]{x^{3}}-\frac{4}{3} x^{\frac{1}{2}}$

\begin{aligned} & \frac{d}{d x}\left(-\frac{1}{2} x^{\frac{7}{2}}+\frac{3}{4} x^{\frac{3}{4}}-\frac{4}{3} x^{\frac{1}{2}}\right) \\ =&-\left(\frac{7}{2}\right)\left(\frac{1}{2}\right) x^{\left(\frac{7}{2}-1\right)} \\ &+\left(\frac{3}{4}\right)\left(\frac{3}{4}\right) x^{\left(\frac{3}{4}-1\right)} \\ &-\left(\frac{1}{2}\right)\left(\frac{4}{3}\right) x^{\left(\frac{1}{2}-1\right)} \end{aligned}
We write the final answer with positive exponents:
$g^{\prime}(x)=-\frac{7}{4} x^{\frac{5}{2}}+\frac{9}{16 x^{\frac{1}{4}}}-\frac{2}{3 x^{\frac{1}{2}}}$
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