4.   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): ( ax + b ) ( cx + d )^2

Answers (1)

Given,

f(x)=( ax + b ) ( cx + d )^2

f(x)=( ax + b ) ( c^2x^2+2cdx+d^2)

f(x)=ac^2x^3+2acdx^2+ad^2x+bc^2x^2+2bcdx+bd^2

Now,

As we know, the property,

f'(x^n)=nx^{n-1}

and the property 

\frac{d(y_1+y_2)}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}

applying that property we get

f'(x)=3ac^2x^2+4acdx+ad^2+2bc^2x+2bcd+0

f'(x)=3ac^2x^2+4acdx+ad^2+2bc^2x+2bcd

f'(x)=3ac^2x^2+(4acd+2bc^2)x+ad^2+2bcd

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