Exercise
$\frac{d}{dx}\left(x\sin\left(x\right)^4-x\sin\left(x\right)^2\right)$
Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(xsin(x)^4-xsin(x)^2) using the sum rule. 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. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sin\left(x\right)^4. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\sin\left(x\right)^2.
Find the derivative d/dx(xsin(x)^4-xsin(x)^2) using the sum rule
Final answer to the exercise
$\sin\left(x\right)^4+4x\sin\left(x\right)^{3}\cos\left(x\right)-\sin\left(x\right)^2-x\sin\left(2x\right)$