Question

differenciate (sin^4x^2+cos^4x^2)^1/2

Answer 1

$$\begin{gathered} \frac{d}{dx}({\sin }^4{x}^2+{\cos }^4{x}^2{)}^{1/2} \\ =\frac{1}{2\sqrt{{\sin }^4{x}^2+{\cos }^4{x}^2}}\times \frac{d}{dx}({\sin }^4{x}^2+{\cos }^4{x}^2) \\ =\frac{1}{2\sqrt{{\sin }^4{x}^2+{\cos }^4{x}^2}}\times \{(4{\sin }^3{x}^2\times \cos x^2\times 2x)+(4{\cos }^3{x}^2\times (-\sin x^2)\times 2x)\} \\ =\frac{4{\sin }^3{x}^2\times \cos x^2\times 2x}{2\sqrt{{\sin }^4{x}^2+{\cos }^4{x}^2}}-\frac{4{\cos }^3{x}^2\times (-\sin x^2)\times 2x}{2\sqrt{{\sin }^4{x}^2+{\cos }^4{x}^2}}(Ans) \end{gathered}$$