Solving: $\frac{d}{dx}\left(\left(3x-1\right)\left(5x-2\right)^{-1}\right)$
Exercise
$\frac{dy}{dx}\left(\left(3x-1\right)\left(5x-2\right)^{-1}\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative of (3x-1)(5x-2)^(-1). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=3x-1 and g=\left(5x-2\right)^{-1}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Simplify the product -(3x-1). The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Find the derivative of (3x-1)(5x-2)^(-1)
Final answer to the exercise
$\frac{3}{5x-2}+\frac{5\left(-3x+1\right)}{\left(5x-2\right)^{2}}$