Exercise
$\frac{d}{dx}\sqrt{\ln\sqrt{\cos^3x}}$
Step-by-step Solution
Learn how to solve power rule for derivatives problems step by step online. Find the derivative of ln(cos(x)^3^(1/2))^(1/2). Simplify the derivative by applying the properties of logarithms. 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 natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Multiplying fractions \frac{1}{2} \times \frac{1}{\sqrt{\cos\left(x\right)^{3}}}.
Find the derivative of ln(cos(x)^3^(1/2))^(1/2)
Final answer to the exercise
$\frac{-3\tan\left(x\right)}{4\sqrt{\ln\left(\sqrt{\cos\left(x\right)^{3}}\right)}}$