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

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

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

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 | 2 years ago