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Exercise

$\frac{d}{dx}10e^{5x^2+1}x$

Step-by-step Solution

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of 10e^(5x^2+1)x. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{\left(5x^2+1\right)} and g=x. The derivative of the linear function is equal to 1. Applying the derivative of the exponential function.
Find the derivative of 10e^(5x^2+1)x

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Final answer to the exercise

$100e^{\left(5x^2+1\right)}x^2+10e^{\left(5x^2+1\right)}$

Try other ways to solve this exercise

  • Choose an option
  • 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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Similar Questions Solved

$\frac{d}{dx}\left(\sqrt{\frac{x\left(x+2\right)}{\left(2x+1\right)\left(5x+3\right)}}\right)$

$\frac{d}{dx}\left(x\sqrt{x^2+1}\right)$

$\frac{d}{dx}\left(2x+1\right)^3$

$\frac{d}{dx}\left(\arcsin\left(1-2x^2\right)\right)$

$\frac{d}{dx}\left(\sqrt{x+1}\right)$

$\frac{d}{dx}\left(x^2+y^2\right)$

$\frac{d}{dx}\left(\arctan\left(x-\sqrt{1+x^2}\right)\right)$

Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

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