Exercise
$\frac{d}{dx}\left(\left(8x^2-16x+16\right)e^{-5x}\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative of (8x^2-16x+16)e^(-5x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=8x^2-16x+16 and g=e^{-5x}. Applying the derivative of the exponential function. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1.
Find the derivative of (8x^2-16x+16)e^(-5x)
Final answer to the exercise
$\left(16x-16\right)e^{-5x}-5\left(8x^2-16x+16\right)e^{-5x}$