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

Derivative of $$$n - p$$$ with respect to $$$n$$$

The calculator will find the derivative of $$$n - p$$$ with respect to $$$n$$$, 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 $$$\frac{d}{dn} \left(n - p\right)$$$.

Solution

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

$${\color{red}\left(\frac{d}{dn} \left(n - p\right)\right)} = {\color{red}\left(\frac{d}{dn} \left(n\right) - \frac{dp}{dn}\right)}$$

Apply the power rule $$$\frac{d}{dn} \left(n^{m}\right) = m n^{m - 1}$$$ with $$$m = 1$$$, in other words, $$$\frac{d}{dn} \left(n\right) = 1$$$:

$${\color{red}\left(\frac{d}{dn} \left(n\right)\right)} - \frac{dp}{dn} = {\color{red}\left(1\right)} - \frac{dp}{dn}$$

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

$$1 - {\color{red}\left(\frac{dp}{dn}\right)} = 1 - {\color{red}\left(0\right)}$$

Thus, $$$\frac{d}{dn} \left(n - p\right) = 1$$$.

Answer

$$$\frac{d}{dn} \left(n - p\right) = 1$$$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