12.  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 ) ^ n

Answers (1)

Given

f(x)=( ax + b ) ^ n

Now, As we know the chain rule of derivative,

[f(g(x))]'=f'(g(x))\times g'(x)

And, the property,

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

Also the property 

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

applying those properties we get,

f'(x)=n(ax+b)^{n-1}\times a

f'(x)=an(ax+b)^{n-1}

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