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Derivative of $$$4 x$$$

The calculator will find the derivative of $$$4 x$$$, with steps shown.

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

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Your Input

Find $$$\frac{d}{dx} \left(4 x\right)$$$.

Solution

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

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

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

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

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

Answer

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

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