Solve left(y^2right)^2(4y)

$${ \left( { y }^{ 2 } \right) }^{ 2 } (4y)$$

Evaluate

$$4y^{5}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$y^{4}\times 4y$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$y^{5}\times 4$$

Differentiate w.r.t. y

$$20y^{4}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{4}\times 4y)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y^{5}\times 4)$$

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

$$5\times 4y^{5-1}$$

Multiply 5 times 4.

$$20y^{5-1}$$

Subtract 1 from 5.

$$20y^{4}$$