Question

Differentiate using chain rule


f(x) = sin(
${3x}^{2}$
+ x)​

Answer 1

ANSWER:

$f'(x) =(6x+ 1) \cos({3x}^{2}+ x)$

GIVEN:

$f(x) = sin({3x}^{2}+ x)$

TO FIND:

• The value of f'(x).

EXPLANATION:

$f(x) = sin({3x}^{2}+ x)$

Differentiate w.r.t x

$\dfrac{d}{dx} f(x) = \dfrac{d}{dx} sin({3x}^{2}+ x)$

$\sf {\boxed{\bold{\large{\blue{\dfrac{d}{dx} f(x) = f'(x)}}}}}$

$\sf {\boxed{\bold{\large{\red{\dfrac{d}{dx} \sin x=\cos x}}}}}$

$f'(x) = \cos({3x}^{2}+ x) \dfrac{d}{dx} ({3x}^{2}+ x)$

$\sf {\boxed{\bold{\large{\orange{\dfrac{d}{dx} {x}^{2} = 2x}}}}}$

$\sf {\boxed{\bold{\large{\pink{\dfrac{d}{dx} x =1}}}}}$

$f'(x) = \cos({3x}^{2}+ x) (6x+ 1) \dfrac{d}{dx} x$

$f'(x) =(6x+ 1) \cos({3x}^{2}+ x)$