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Solving: ddx(xtan⁡(3x))\frac{d}{dx}\left(x^{\tan\left(3x\right)}\right)
Solve instead: dydxxtan⁡(3x)\frac{dy}{dx}x^{\tan\left(3x\right)}
f(x)=x^tan(3x)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

dydxxtan⁡(3x)\frac{dy}{dx}x^{\tan\left(3x\right)}

Step-by-step Solution

Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(x^tan(3x)). To derive the function x^{\tan\left(3x\right)}, use the method of logarithmic differentiation. First, assign the function to y, then take the natural logarithm of both sides of the equation. Apply natural logarithm to both sides of the equality. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Derive both sides of the equality with respect to x.
Find the derivative using logarithmic differentiation method d/dx(x^tan(3x))

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Final answer to the exercise

(3sec⁡(3x)2ln⁡(x)+tan⁡(3x)x)xtan⁡(3x)\left(3\sec\left(3x\right)^2\ln\left(x\right)+\frac{\tan\left(3x\right)}{x}\right)x^{\tan\left(3x\right)}

Try other ways to solve this exercise

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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
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  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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dydx xtan(3x)
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