Solve d/dxleft(2x^2+4right)(4x)

$$\frac{d}{d x } \left(2 { x }^{ 2 } +4 \right) (4x)$$

Evaluate

$$24x^{2}+16$$

Steps Using Derivative Rule for Sum

Use the distributive property to multiply 2x^{2}+4 by 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(8x^{2}+16\right)x)$$

Use the distributive property to multiply 8x^{2}+16 by x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{3}+16x)$$

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}.

$$3\times 8x^{3-1}+16x^{1-1}$$

Multiply 3 times 8.

$$24x^{3-1}+16x^{1-1}$$

Subtract 1 from 3.

$$24x^{2}+16x^{1-1}$$

Subtract 1 from 1.

$$24x^{2}+16x^{0}$$

For any term t except 0, t^{0}=1.

$$24x^{2}+16\times 1$$

For any term t, t\times 1=t and 1t=t.

$$24x^{2}+16$$

Differentiate w.r.t. x

$$48x$$