No AI is used
  1. Home
  2. Calculators
  3. Calculators: Calculus I
  4. Calculus Calculator

Derivative of $$$\cos{\left(t \right)} + 1$$$

The calculator will find the derivative of $$$\cos{\left(t \right)} + 1$$$, with steps shown.

Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps

Leave empty for autodetection.
Leave empty, if you don't need the derivative at a specific point.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Your Input

Find $$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right)$$$.

Solution

The derivative of a sum/difference is the sum/difference of derivatives:

$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right) + \frac{d}{dt} \left(1\right)\right)}$$

The derivative of a constant is $$$0$$$:

$${\color{red}\left(\frac{d}{dt} \left(1\right)\right)} + \frac{d}{dt} \left(\cos{\left(t \right)}\right) = {\color{red}\left(0\right)} + \frac{d}{dt} \left(\cos{\left(t \right)}\right)$$

The derivative of the cosine is $$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$:

$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)} = {\color{red}\left(- \sin{\left(t \right)}\right)}$$

Thus, $$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right) = - \sin{\left(t \right)}$$$.

Answer

$$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right) = - \sin{\left(t \right)}$$$A


Please try a new game Rotatly
Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function