Solve 7x^32^3

$$7 x ^ { 3 } 2 ^ { 3 }$$

Evaluate

$$56x^{3}$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$7x^{3}\times 8$$

Multiply 7 and 8 to get 56.

$$56x^{3}$$

Differentiate w.r.t. x

$$168x^{2}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}\times 8)$$

Multiply 7 and 8 to get 56.

$$\frac{\mathrm{d}}{\mathrm{d}x}(56x^{3})$$

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

$$3\times 56x^{3-1}$$

Multiply 3 times 56.

$$168x^{3-1}$$

Subtract 1 from 3.

$$168x^{2}$$