Exercise
$\frac{d}{dx}\sin^3\:.\:3x$
Step-by-step Solution
Learn how to solve problems step by step online. Find the derivative of sin(x)^33x. 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=\sin\left(x\right)^3 and g=x. The derivative of the linear function is equal to 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}.
Find the derivative of sin(x)^33x
Final answer to the exercise
$9x\sin\left(x\right)^{2}\cos\left(x\right)+3\sin\left(x\right)^3$