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- Find the derivative using the definition
- Find the derivative using the product rule
- Find the derivative using the quotient rule
- Find the derivative using logarithmic differentiation
- Find the derivative
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x^9$ and $g=\cos\left(x\right)$
Learn how to solve differential calculus problems step by step online.
$\frac{d}{dx}\left(x^9\right)\cos\left(x\right)+x^9\frac{d}{dx}\left(\cos\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of x^9cos(x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^9 and g=\cos\left(x\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Subtract the values 9 and -1. 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).
