For some constants a and b, find the derivative of (ax2 + b)2

Asked by Pragya Singh | 1 year ago |  57

##### Solution :-

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

$$f'(x)=\dfrac{d}{dx}(a^2x^4+2abx^2+b^2)$$

$$a^2\dfrac{d}{dx}(x^4)+2ab\dfrac{d}{dx}(x^2)+\dfrac{d}{dx}b^2$$

On using theorem $$\dfrac{d}{dx}(x^n)=nx^{n-1}$$, we obtain

$$f'(x)=a^2(4x^3)+2ab(2x)+b^2(0)$$

$$4a^2x^3+4abx$$

$$4ax(ax^2+b)$$

Answered by Abhisek | 1 year ago

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