Solve (xe^lnx^2)

$$( x e ^ { \ln x ^ { 2 } } )$$

Evaluate

$$x^{3}$$

Solution Steps

Apply rule a^{\log_{a}\left(b\right)}=b, where a=e and b=x^{2}.

$$xx^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Steps Using Definition of a Derivative

Apply rule a^{\log_{a}\left(b\right)}=b, where a=e and b=x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(xx^{2})$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3})$$

The derivative of ax^{n} is nax^{n-1}.

$$3x^{3-1}$$

Subtract 1 from 3.

$$3x^{2}$$