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Exercise

$\frac{d}{dx}5^{6x}$

Step-by-step Solution

1

Applying the derivative of the exponential function

$\ln\left(5\right)5^{6x}\frac{d}{dx}\left(6x\right)$
2

The derivative of a function multiplied by a constant ($6$) is equal to the constant times the derivative of the function

$6\ln\left(5\right)5^{6x}\frac{d}{dx}\left(x\right)$
3

The derivative of the linear function is equal to $1$

$6\ln\left(5\right)5^{6x}$

Final answer to the exercise

$6\ln\left(5\right)5^{6x}$

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
  • Load more...
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Similar Questions Solved

$\frac{d}{dx}\tan\left(x\right)$

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

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

$\frac{d}{dx}\sin\left(3x\right)$

$\frac{d}{dx}\sin\left(x\right)\cos\left(x\right)$

$\frac{d}{dx}\left(ln\left(cos\left(x\right)\right)\right)$

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

Main Topic: Basic Differentiation Rules

Some differentiation rules are very easy to remember and use. These are the basic ones: constant rule, sum rule, product rule and quotient rule.

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