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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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The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function
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$-\frac{1}{5}\frac{d}{dx}\left(\csc\left(x^2-1\right)^5\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of -1/5csc(x^2-1)^5. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Multiply the fraction and term in 5\left(-\frac{1}{5}\right)\csc\left(x^2-1\right)^{4}\frac{d}{dx}\left(\csc\left(x^2-1\right)\right). Taking the derivative of cosecant function: \frac{d}{dx}\left(\csc(x)\right)=-\csc(x)\cdot\cot(x)\cdot D_x(x).