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Derivative of 2x22 x^{2}

The calculator will find the derivative of 2x22 x^{2}, with steps shown.

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

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Your Input

Find ddx(2x2)\frac{d}{dx} \left(2 x^{2}\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=2c = 2 and f(x)=x2f{\left(x \right)} = x^{2}:

(ddx(2x2))=(2ddx(x2)){\color{red}\left(\frac{d}{dx} \left(2 x^{2}\right)\right)} = {\color{red}\left(2 \frac{d}{dx} \left(x^{2}\right)\right)}

Apply the power rule ddx(xn)=nxn−1\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1} with n=2n = 2:

2(ddx(x2))=2(2x)2 {\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} = 2 {\color{red}\left(2 x\right)}

Thus, ddx(2x2)=4x\frac{d}{dx} \left(2 x^{2}\right) = 4 x.

Answer

ddx(2x2)=4x\frac{d}{dx} \left(2 x^{2}\right) = 4 xA

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