Solve 4(x^3)^4

$$4 ( x ^ { 3 } ) ^ { 4 }$$

Differentiate w.r.t. x

$$48x^{11}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{12})$$

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

$$12\times 4x^{12-1}$$

Multiply 12 times 4.

$$48x^{12-1}$$

Subtract 1 from 12.

$$48x^{11}$$

Evaluate

$$4x^{12}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$4x^{12}$$