Differentiate $y={{\cos }^{4}}\left( 2{{x}^{2}}+1 \right)-\sin x$ with respect to $x$. Hence, fi

Question

Differentiate $y={{\cos }^{4}}\left( 2{{x}^{2}}+1 \right)-\sin x$ with respect to $x$. Hence, find $\displaystyle\int{x\sin \left( 2{{x}^{2}}+1 \right){{\cos }^{3}}\left( 2{{x}^{2}}+1 \right)}\,\mathrm{d}x$.

Accepted Answer

(i) $-16x\sin(2x^2+1)\cos^3(2x^2+1)-\cos x$. (ii) $-\frac1{16}\cos^4(2x^2+1)+C$.

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

Solution:

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