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  • For some constants a and b, find the derivative of ax ^2 + b ^2

7.(ii)   For some constants a and b, find the derivative of ( ax ^2 + b)^2

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best_answer

Given 

f(x)=( ax ^2 + b)^2=a^2x^4+2abx^2+b^2

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 those properties we get 

f'(x)=4a^2x^3+2(2)abx+0

f'(x)=4a^2x^3+4abx

f'(x)=4ax(ax^2+b)

 

Posted by

Pankaj Sanodiya

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