Find the derivative with respect to the independent variable.

$f\left(x\right)=9\mathrm{cos}x-2\mathrm{sin}x$

f'(x)=

f'(x)=

sklicatias
2021-11-21
Answered

Find the derivative with respect to the independent variable.

$f\left(x\right)=9\mathrm{cos}x-2\mathrm{sin}x$

f'(x)=

f'(x)=

You can still ask an expert for help

romancemrf

Answered 2021-11-22
Author has **14** answers

Step 1

We have to find derivatives of function:

$f\left(x\right)=9\mathrm{cos}x-2\mathrm{sin}x$

We know the derivatives of trigonometric ratios:

$\frac{d\mathrm{cos}x}{dx}=-\mathrm{sin}x$

$\frac{d\mathrm{sin}x}{dx}=\mathrm{cos}x$

Step 2

So differentiating the function$f\left(x\right)=9\mathrm{cos}x-2\mathrm{sin}x$ with respect to 'x', we get

$f\left(x\right)=9\mathrm{cos}x-2\mathrm{sin}x$

$f}^{\prime}\left(x\right)=9\frac{d\mathrm{cos}x}{dx}-2\frac{d\mathrm{sin}x}{dx$

$=9(-\mathrm{sin}x)-2\left(\mathrm{cos}x\right)$

$=-9\mathrm{sin}-2\mathrm{cos}x$

Hence, value of${f}^{\prime}\left(x\right)\text{}is\text{}-9\mathrm{sin}-2\mathrm{cos}x$ .

We have to find derivatives of function:

We know the derivatives of trigonometric ratios:

Step 2

So differentiating the function

Hence, value of

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(a) f ' (0)1

(b) f ' (1)2

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(d) f ' (3)4

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(a) f ' (0)1

(b) f ' (1)2

(c) f ' (2)3

(d) f ' (3)4

(e) f ' (4)5

(f) f ' (5)6

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