Derivative of xnx^{n} with respect to xx

The calculator will find the derivative of xnx^{n} with respect to xx, with steps shown.

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Your Input

Find ddx(xn)\frac{d}{dx} \left(x^{n}\right).

Solution

Apply the power rule ddx(xm)=mxm1\frac{d}{dx} \left(x^{m}\right) = m x^{m - 1} with m=nm = n:

(ddx(xn))=(nxn1){\color{red}\left(\frac{d}{dx} \left(x^{n}\right)\right)} = {\color{red}\left(n x^{n - 1}\right)}

Thus, ddx(xn)=nxn1\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}.

Answer

ddx(xn)=nxn1\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}A