Deutsch | Español | Português | Français | Italiano | Polski | Українська
  1. Home
  2. Calculators
  3. Calculators: Calculus I
  4. Calculus Calculator

Derivative of 4x4 x

The calculator will find the derivative of 4x4 x, 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 ddx(4x)\frac{d}{dx} \left(4 x\right).

Solution

Apply the constant multiple rule ddx(cf(x))=cddx(f(x))\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right) with c=4c = 4 and f(x)=xf{\left(x \right)} = x:

(ddx(4x))=(4ddx(x)){\color{red}\left(\frac{d}{dx} \left(4 x\right)\right)} = {\color{red}\left(4 \frac{d}{dx} \left(x\right)\right)}

Apply the power rule ddx(xn)=nxn−1\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1} with n=1n = 1, in other words, ddx(x)=1\frac{d}{dx} \left(x\right) = 1:

4(ddx(x))=4(1)4 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = 4 {\color{red}\left(1\right)}

Thus, ddx(4x)=4\frac{d}{dx} \left(4 x\right) = 4.

Answer

ddx(4x)=4\frac{d}{dx} \left(4 x\right) = 4A

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