Final answer to the problem
$\frac{-1}{x\sqrt{25x^2-1}\mathrm{arcsec}\left(5x\right)^{2}}$
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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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The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$
Learn how to solve differential calculus problems step by step online.
$-\mathrm{arcsec}\left(5x\right)^{-2}\frac{d}{dx}\left(\mathrm{arcsec}\left(5x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of arcsec(5x)^(-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}. Taking the derivative of arcsecant. The power of a product is equal to the product of it's factors raised to the same power. Multiplying the fraction by -1.
Final answer to the problem
$\frac{-1}{x\sqrt{25x^2-1}\mathrm{arcsec}\left(5x\right)^{2}}$
