## anonymous 5 years ago derivative of 5x^cos (x^x)

1. anonymous

****5x^cos(x^2)

2. anonymous

Take the logarithm of both sides first, and then apply the derivative operator:$y=5x^{\cos x^2} \rightarrow \ln y=\ln 5+\cos (x^2) \ln x$

3. anonymous

Then$\frac{y'}{y}=\frac{\cos(x^2)}{x}+\ln x \times -\sin(x^2) \times 2x$

4. anonymous

Multiply both sides by y = 5x^(cos(x^2)) to get$y'=5x^{\cos{x^2}}\left[ \frac{\cos (x^2)}{x}-2x \sin (x^2) \ln x \right]$

5. anonymous

Just check my working...rushing...