If y=(3x³-5x²+8)³ then \;dy/dx is

Correct Answer is : 3(3x3−5x2+8)2(9x2−10x)3(3x³-5x²+8)²(9x²-10x)3(3x3−5x2+8)2(9x2−10x)

Correct Answer is : 3(3x3−5x2+8)2(9x2−10x)3(3x³-5x²+8)²(9x²-10x)3(3x3−5x2+8)2(9x2−10x)

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Differential Calculus

Question : 57 of 69

Marks: +1, -0

y=(3x^{3}-5x^{2}+8)^{3}

\;\frac{dy}{dx}

Solution:

Concept:

Apply the chain rule: differentiate the outer power function and multiply by the derivative of the inner polynomial.

Explanation:

Given

y = (3x^{3} - 5x^{2} + 8)^{3}

Let

u = 3x^{3} - 5x^{2} + 8

, so

y = u^{3}

Then

\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = 3u^{2} \cdot (9x^{2} - 10x)

Substitute back

u

\frac{dy}{dx} = 3(3x^{3} - 5x^{2} + 8)^{2}(9x^{2} - 10x)

Answer:

Option A:

3(3x^{3}-5x^{2}+8)^{2}(9x^{2}-10x)

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