Solve (x^3)^4*x^2=

$$( x ^ { 3 } ) ^ { 4 } \cdot x ^ { 2 } =$$

Evaluate

$$x^{14}$$

Solution Steps

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

$$x^{12}x^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$x^{14}$$

Differentiate w.r.t. x

$$14x^{13}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12}x^{2})$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{14})$$

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

$$14x^{14-1}$$

Subtract 1 from 14.

$$14x^{13}$$