Find the derivative of the following function:
f(x)= $(a x^{2} + s i n x) (p + q c o s x)$

Open in App

Solution

Here f(x) = $(a x^{2} + s i n x) (p + q c o s x)$

$∴ f^{'} (x) = \frac{d}{d x} [(a x^{2} + s i n x) (p + q c o s x)]$

$= (a x^{2} + s i n x) \frac{d}{d x} (p + q c o s x) + (p + q c o s x) \frac{d}{d x} (a x^{2} + s i n x)$

$= (a x^{2} + s i n x) (- q s i n x) + (p + q c o s x) (2 a x + c o s x)$

$= q s i n x (a x^{2} - s i n x) + (p + q c o s x) (2 a x + c o s x)$ .

Suggest Corrections

Similar questions

Q. Find the derivative of

(a x^{2} + sin x) (p + q cos x)

where

a, p, q

are fixed non-zero constants.

Q. 24. (ax2 + sinx)(p+ qcosx)

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax² + sin x) (p + q cos x)

Q. Find the derivative of the following functions (it is to be understood that

a, b, c, d, p, q, r

and

s

are fixed non-zero constants and

m

and

n

are integers) :

(a x^{2} + sin x) (p + q cos x)

Q. Find the derivative of the following function:
f(x)=

\frac{1}{a x^{2} + b x + c}

Join BYJU'S Learning Program

Find the derivative of the following function: f(x)= (ax2+sin x)(p+q cos x)

Here f(x) = (ax2+sin x)(p+q cos x) ∴f′(x)=ddx[(ax2+sin x)(p+q cos x)] =(ax2+sin x)ddx(p+q cos x)+(p+q cos x)ddx(ax2+sin x) =(ax2+sin x)(−q sin x)+(p+q cos x)(2ax+cos x) =q sin x(ax2−sin x)+(p+q cos x)(2ax+cosx).

Find the derivative of the following function:
f(x)= $(a x^{2} + s i n x) (p + q c o s x)$