Exercise
$\frac{d}{dx}\left(\ln\left(\frac{\sqrt{-x+4}}{e^{x^2}cos\left(3x^2+x\right)}\right)\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative of ln(((-x+4)^(1/2))/(e^x^2cos(3x^2+x))). Simplify the derivative by applying the properties of logarithms. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Find the derivative of ln(((-x+4)^(1/2))/(e^x^2cos(3x^2+x)))
Final answer to the exercise
$\frac{-1}{2\left(-x+4\right)}-2x+\left(6x+1\right)\tan\left(3x^2+x\right)$