Question

differentiation of this

Answer 1

Let,

$y = (3x - 4) ^ { \frac{3}{2} }$

Now, let,

$u= (3x - 4)$

and, thus;

$y = u {}^{ \frac{3}{2} }$

★To Find★

$\frac{d}{dx} (y)$

★Solution★

Using the chain Rule:

$y'= \frac{dy}{du} \times \frac{du}{dx}$

$y' = \frac{d}{du} (u {}^{ \frac{3}{2} } ) \times \frac{d}{dx} (3x - 4)$

$y' = \frac{3}{2} (u {}^{ \frac{3}{2} - 1} ) \times (3)$

$y' = \frac{9}{2} (u {}^{ \frac{1}{2} })$

$y' = \frac{9}{2} ( \sqrt{u} )$

$y' = \frac{9}{2} ( \sqrt{3x - 4} )$

∴ , the derivative of the given expression is given by:

$y' = \frac{9 \sqrt{3x - 4}}{2}$

Answer 2

Explanation:

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