Differentiate this equation (below):

Question

$$\Large y = x^{\ln 7} + \log_7 x $$

I know for differentiating logarithms you do: $1/f(x) \cdot f'(x) \cdot 1/\ln b$. But how about differentiating $x^{\ln 7}$? I don't understand how to change stuff into $e$ and I'm confused about this. Thank you.

Answer 1

$$\frac{d}{dx}(x^n)=nx^{n-1}$$

Now put $n=\ln7$

$$\frac{d}{dx}(x^{\ln7})=(\ln7)x^{\ln7-1}$$