Solve d/dx[2(4x^3+1)-2]^frac{2{3}}

$$\frac { d } { d x } [ 2 ( 4 x ^ { 3 } + 1 ) - 2 ] ^ { \frac { 2 } { 3 } }$$

Evaluate

$$8x$$

Steps Using Definition of a Derivative

Use the distributive property to multiply 2 by 4x^{3}+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(8x^{3}+2-2\right)^{\frac{2}{3}})$$

Subtract 2 from 2 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(8x^{3}\right)^{\frac{2}{3}})$$

Expand \left(8x^{3}\right)^{\frac{2}{3}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8^{\frac{2}{3}}\left(x^{3}\right)^{\frac{2}{3}})$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{2}{3} to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8^{\frac{2}{3}}x^{2})$$

Calculate 8 to the power of \frac{2}{3} and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2})$$

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

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

Multiply 2 times 4.

$$8x^{2-1}$$

Subtract 1 from 2.

$$8x^{1}$$

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

$$8x$$

Differentiate w.r.t. x

$$8$$