Question

if f(x)=sinx° then find f'(x)​

Answer 1

Given,

A function f(x) = sin x

To Find,

The value of f'(x)

Solution,

To find the value of f'(x) we need to differentiate the function f(x) sin x.

Now,

The differentiation of the function f(x) = sin x is cos x

f(x) = sin x

f'(x) = d(sinx)/dx = cos x dx/dx = cos x

Hence, the value of f'(x) is cos x.

Answer 2

$\displaystyle \sf{ f '(x) = \frac{\pi x}{180} cos \: {x}^{ \circ} }$

Given :

$\displaystyle \sf{ f (x) = sin \: {x}^{ \circ} }$

To find :

The value of f'(x)

Solution :

Step 1 of 2 :

Write down the given function

Here the given function is

$\displaystyle \sf{ f (x) = sin \: {x}^{ \circ} }$

$\displaystyle \sf{ \implies f(x) = sin \: \frac{\pi x}{180} }$

Step 2 of 2 :

Find the value of f'(x)

$\displaystyle \sf{ f(x) = sin \: \frac{\pi x}{180} }$

Differentiating both sides with respect to x we get

$\displaystyle \sf{ f'(x) = \frac{d}{dx} \bigg( sin \: \frac{\pi x}{180}\bigg) }$

$\displaystyle \sf{ \implies f'(x) = cos \:\frac{\pi x}{180} \: \times \frac{d}{dx} \bigg( \frac{\pi x}{180}\bigg)}$

$\displaystyle \sf{ \implies f'(x) = cos \:\frac{\pi x}{180} \: \times \frac{\pi }{180} \frac{d}{dx} \bigg( x\bigg)}$

$\displaystyle \sf{ \implies f'(x) = cos \:\frac{\pi x}{180} \: \times \frac{\pi }{180} \times 1}$

$\displaystyle \sf{ \implies f'(x) =\frac{\pi }{180} cos \:\frac{\pi x}{180} \: }$

$\displaystyle \sf{ \implies f '(x) = \frac{\pi x}{180} cos \: {x}^{ \circ}}$

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