Answer
$y^\prime=10x^{10x}(1+ln(x))$
Work Step by Step
If we let the function we are trying to differentiate be equal to y we have: $y=x^{10x}$, now we can use logarithmic differentiation. Start by taking the natural log of both sides: $ln(y)=ln(x^{10x})=10xln(x)$ Now if we differentiate both sides using the product rule we get: $\dfrac{y^\prime}{y}=10ln(x)+10$ now we need to multiply both sides of the equation by y which is just $x^{10x}$ so: $ y^\prime=x^{10x}(10ln(x)+10)=10x^{10x}(1+ln(x))$
