Find the derivative of $f(x)=\frac{1}{\left(2 x^{5}+\sin x\right)^{3}}$
$f^{\prime}(x)=\frac{-3}{\left(2 x^{5}+\sin x\right)^{4}}$
$f^{\prime}(x)=\frac{-3}{\left(10 x^{4}+\cos x\right)^{4}}$
$f^{\prime}(x)=\frac{-3\left(10 x^{4}+\cos x\right)}{\left(2 x^{5}+\sin x\right)^{2}}$
$f^{\prime}(x)=\frac{-3\left(10 x^{4}+\cos x\right)}{\left(2 x^{5}+\sin x\right)^{4}}$

Step 1 ：Given the function \(f(x)=\frac{1}{\left(2 x^{5}+\sin x\right)^{3}}\), we are asked to find its derivative.

Step 2 ：First, we need to find the derivative of the outer function, which is \(\frac{1}{\left(2 x^{5}+\sin x\right)^{3}}\). Using the power rule, the derivative of this function is \(-3\left(2 x^{5}+\sin x\right)^{-4}\).

Step 3 ：Next, we need to find the derivative of the inner function, which is \(2 x^{5}+\sin x\). The derivative of \(2 x^{5}\) is \(10x^{4}\) and the derivative of \(\sin x\) is \(\cos x\). So, the derivative of the inner function is \(10x^{4}+\cos x\).

Step 4 ：Finally, we multiply the derivative of the outer function by the derivative of the inner function to get the derivative of the original function. This gives us \(f^\prime(x)=\frac{-3\left(10 x^{4}+\cos x\right)}{\left(2 x^{5}+\sin x\right)^{4}}\).

Step 5 ：\(\boxed{f^\prime(x)=\frac{-3\left(10 x^{4}+\cos x\right)}{\left(2 x^{5}+\sin x\right)^{4}}}\) is the final answer.