Final answer to the problem
$5\sec\left(5x\right)\tan\left(5x\right)$
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Step-by-step Solution
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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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1
Taking the derivative of secant function: $\frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x)$
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$\frac{d}{dx}\left(5x\right)\sec\left(5x\right)\tan\left(5x\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of sec(5x). Taking the derivative of secant function: \frac{d}{dx}\left(\sec(x)\right)=\sec(x)\cdot\tan(x)\cdot D_x(x). The derivative of a function multiplied by a constant (5) is equal to the constant times the derivative of the function. The derivative of the linear function is equal to 1.
Final answer to the problem
$5\sec\left(5x\right)\tan\left(5x\right)$
