FizeauV

2021-10-04

Calculating derivatives Find dy>dx for the following functions.

$y=5{x}^{2}+\mathrm{cos}x$

liingliing8

Skilled2021-10-05Added 95 answers

Step 1

To find:

The derivative of$y=5{x}^{2}+\mathrm{cos}x$ .

Formula used:

Sum rule of derivative:

$\frac{d}{dx}(u+v)=\frac{d}{dx}\left(u\right)+\frac{d}{dx}\left(v\right)$

Power rule of derivative:

$\left({x}^{n}\right)}^{\prime}=n\cdot {x}^{n-1$

Trigonometric function derivative:

${\left(\mathrm{cos}x\right)}^{\prime}=-\mathrm{sin}x$

Step 2

Calculation:

The derivative of$y=5{x}^{2}+\mathrm{cos}x$ can be obtained as,

$\frac{dy}{dx}=\frac{d}{dx}(5{x}^{2}+\mathrm{cos}x)$

$=\frac{d}{dx}\left(5{x}^{2}\right)+\frac{d}{dx}\left(\mathrm{cos}x\right)$

$=5(2\cdot {x}^{2-1})-\mathrm{sin}x$

$=10x-\mathrm{sin}x$

Thus, the value is$\frac{dy}{dx}=10x-\mathrm{sin}x$ .

To find:

The derivative of

Formula used:

Sum rule of derivative:

Power rule of derivative:

Trigonometric function derivative:

Step 2

Calculation:

The derivative of

Thus, the value is

Jeffrey Jordon

Expert2022-08-15Added 2575 answers