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

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

Evaluate

$$y^{13}$$

Solution Steps

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

$$yy^{6}\left(y^{3}\right)^{2}$$

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

$$yy^{6}y^{6}$$

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

$$y^{7}y^{6}$$

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$y^{13}$$

Differentiate w.r.t. y

$$13y^{12}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(yy^{6}\left(y^{3}\right)^{2})$$

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{7}y^{6})$$

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{13})$$

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

$$13y^{13-1}$$

Subtract 1 from 13.

$$13y^{12}$$