What is the derivative of $f (x) = cos (π \cdot x^{2})$ $f(x)=cos(pi*x^2)$ ?

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What is the derivative of $f (x) = cos (π \cdot x^{2})$ $f(x)=cos(pi*x^2)$ ?

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Answer 1 · 2015-12-05T16:17:44

$- 2 π x sin (π x^{2})$ $-2pixsin(pix^2)$

Explanation:

From standard rules of differentiation, the derivative of the cosine of a function is the negative sine of the function multiplied by the derivative of the function.

Applying this rule yields :

$\frac{d}{d x} cos (π x^{2}) = - sin (π x^{2}) \cdot \frac{d}{d x} π x^{2}$ $d/dxcos(pix^2)=-sin(pix^2)*d/dxpix^2$

$= - sin (π x^{2}) \cdot 2 π x$ $=-sin(pix^2)*2pix$

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What is the derivative of $f (x) = cos (π \cdot x^{2})$ $f(x)=cos(pi*x^2)$ ?

1 Answer

Explanation:

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