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Derivative of 3x3 x

The calculator will find the derivative of 3x3 x, with steps shown.

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

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Your Input

Find ddx(3x)\frac{d}{dx} \left(3 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=3c = 3 and f(x)=xf{\left(x \right)} = x:

(ddx(3x))=(3ddx(x)){\color{red}\left(\frac{d}{dx} \left(3 x\right)\right)} = {\color{red}\left(3 \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:

3(ddx(x))=3(1)3 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = 3 {\color{red}\left(1\right)}

Thus, ddx(3x)=3\frac{d}{dx} \left(3 x\right) = 3.

Answer

ddx(3x)=3\frac{d}{dx} \left(3 x\right) = 3A

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