Solve (y^2)^3*y

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

Evaluate

$$y^{7}$$

Solution Steps

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

$$y^{6}y$$

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

$$y^{7}$$

Differentiate w.r.t. y

$$7y^{6}$$

Steps Using Definition of a Derivative

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

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

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

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

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

$$7y^{7-1}$$

Subtract 1 from 7.

$$7y^{6}$$