Expand $\left(25a^{2}\right)^{\frac{1}{2}}$.

To raise a power to another power, multiply the exponents. Multiply $2$ and $\frac{1}{2}$ to get $1$.

Calculate $25$ to the power of $\frac{1}{2}$ and get $5$.

Calculate $a$ to the power of $1$ and get $a$.

If $F$ is the composition of two differentiable functions $f\left(u\right)$ and $u=g\left(x\right)$, that is, if $F\left(x\right)=f\left(g\left(x\right)\right)$, then the derivative of $F$ is the derivative of $f$ with respect to $u$ times the derivative of $g$ with respect to $x$, that is, $\frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right)$.

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is $0$. The derivative of $ax^{n}$ is $nax^{n-1}$.

Simplify.

For any term $t$, $t^{1}=t$.