Solve (x^3)^2*x

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

Evaluate

$$x^{7}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$x^{6}x$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$x^{7}$$

Differentiate w.r.t. x

$$7x^{6}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}x)$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

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

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

$$7x^{7-1}$$

Subtract 1 from 7.

$$7x^{6}$$