Learn how to solve problems step by step online. Find the derivative of cos(sin(2x+5))^(1/2). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). Multiply the fraction and term in -\frac{1}{2}\cos\left(\sin\left(2x+5\right)\right)^{-\frac{1}{2}}\sin\left(\sin\left(2x+5\right)\right)\frac{d}{dx}\left(\sin\left(2x+5\right)\right). The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}.

Find the derivative of cos(sin(2x+5))^(1/2)