Solve (5y)4^

$$(5y) { 4 }^{ }$$

Evaluate

$$20y$$

Solution Steps

Calculate 4 to the power of 1 and get 4.

$$5y\times 4$$

Multiply 5 and 4 to get 20.

$$20y$$

Differentiate w.r.t. y

$$20$$

Steps Using Definition of a Derivative

Calculate 4 to the power of 1 and get 4.

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

Multiply 5 and 4 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}y}(20y)$$

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

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

Subtract 1 from 1.

$$20y^{0}$$

For any term t except 0, t^{0}=1.

$$20\times 1$$

For any term t, t\times 1=t and 1t=t.

$$20$$