Solve 2{left(y^2right)}^frac{1{2}}

$$2 { \left( { y }^{ 2 } \right) }^{ \frac{ 1 }{ 2 } }$$

Evaluate

$$2|y|$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{2} to get 1.

$$2y^{1}$$

Calculate y to the power of 1 and get y.

$$2y$$

Differentiate w.r.t. y

$$2sign(y)$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{2} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2y^{1})$$

Calculate y to the power of 1 and get y.

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

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

$$2y^{1-1}$$

Subtract 1 from 1.

$$2y^{0}$$

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

$$2\times 1$$

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

$$2$$