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