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Exercise

$\frac{d}{dx}\left(cos\left(x+9y\right)\right)$

Step-by-step Solution

1

The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if $f(x) = \cos(x)$, then $f'(x) = -\sin(x)\cdot D_x(x)$

$-\frac{d}{dx}\left(x+9y\right)\sin\left(x+9y\right)$
2

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$-\sin\left(x+9y\right)$

Final answer to the exercise

$-\sin\left(x+9y\right)$

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

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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