How do you find the derivative of $y = cos (a^{3} + x^{3})$ $y = cos(a^3 + x^3)$ using the chain rule?

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How do you find the derivative of $y = cos (a^{3} + x^{3})$ $y = cos(a^3 + x^3)$ using the chain rule?

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Answer 1 · 2016-01-22T08:33:21

$\frac{d y}{d x} = - 3 x^{2} sin (a^{3} + x^{3})$ $dy/dx = -3x^2 sin(a^3 + x^3 )$

Explanation:

using 'chain rule'

$\frac{d y}{d x} = - sin (a^{3} + x^{3}) . \frac{d}{d x} (a^{3} + x^{3})$ $dy/dx = - sin(a^3 + x^3) .d/dx (a^3 + x^3 )$

$= - sin (a^{3} + x^{3}) . (3 x^{2})$ $= - sin( a^3 + x^3 ). (3x^2 )$

$\Rightarrow \frac{d y}{d x} = - 3 x^{2} sin (a^{3} + x^{3})$ $rArr dy/dx = - 3x^2 sin(a^3 +x^3 )$

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How do you find the derivative of $y = cos (a^{3} + x^{3})$ $y = cos(a^3 + x^3)$ using the chain rule?

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How do you find the derivative of y = cos(a^3 + x^3)y=cos(a3+x3)y = cos(a^3 + x^3) using the chain rule?

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How do you find the derivative of $y = cos (a^{3} + x^{3})$ $y = cos(a^3 + x^3)$ using the chain rule?