Question

Math

Posted 3 months ago

`$\frac{d}{d x}\left[3 \cos (x)+4 x^{2}\right]=$`

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Apply the product rule to differentiate $3 \cos(x) + 4 x^2$

step 2

Differentiate $3 \cos(x)$ to get $-3 \sin(x)$

step 3

Differentiate $4 x^2$ to get $8x$

step 4

Combine the derivatives to get the final result: $-3 \sin(x) + 8x$

Answer

$-3 \sin(x) + 8x$

Key Concept

Differentiation of trigonometric and polynomial functions

Explanation

The derivative of a sum of functions is the sum of the derivatives of each function. The derivative of $\cos(x)$ is $-\sin(x)$, and the derivative of $x^2$ is $2x$. The constants are multiplied accordingly.

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