Solve {(e)^ln(1+2x^2)}

$${(e)^{ \ln ( 1+2 { x }^{ 2 } ) }}$$

Differentiate w.r.t. x

$$4x$$

Steps Using Derivative Rule for Sum

Apply rule a^{\log_{a}\left(b\right)}=b, where a=e and b=1+2x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1+2x^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times 2x^{2-1}$$

Multiply 2 times 2.

$$4x^{2-1}$$

Subtract 1 from 2.

$$4x^{1}$$

For any term t, t^{1}=t.

$$4x$$

Evaluate

$$2x^{2}+1$$

Solution Steps

Apply rule a^{\log_{a}\left(b\right)}=b, where a=e and b=1+2x^{2}.

$$1+2x^{2}$$