Solve (y^4)^3*y^2

$$( y ^ { 4 } ) ^ { 3 } \cdot y ^ { 2 }$$

Evaluate

$$y^{14}$$

Solution Steps

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

$$y^{12}y^{2}$$

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

$$y^{14}$$

Differentiate w.r.t. y

$$14y^{13}$$

Steps Using Definition of a Derivative

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

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

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

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

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

$$14y^{14-1}$$

Subtract 1 from 14.

$$14y^{13}$$