Solve 1/100016^0.25y^0.75

$$\frac { 1 } { 1000 } 16 ^ { 0.25 } y ^ { 0.75 }$$

Evaluate

$$\frac{y^{0.75}}{500}$$

Solution Steps

Calculate 16 to the power of 0.25 and get 2.

$$\frac{1}{1000}\times 2y^{0.75}$$

Multiply \frac{1}{1000} and 2 to get \frac{1}{500}.

$$\frac{1}{500}y^{0.75}$$

Differentiate w.r.t. y

$$\frac{3}{2000\sqrt[4]{y}}$$

Steps Using Definition of a Derivative

Calculate 16 to the power of 0.25 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{1000}\times 2y^{0.75})$$

Multiply \frac{1}{1000} and 2 to get \frac{1}{500}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{500}y^{0.75})$$

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

$$0.75\times \frac{1}{500}y^{0.75-1}$$

Multiply 0.75 times \frac{1}{500} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{3}{2000}y^{0.75-1}$$

Subtract 1 from 0.75.

$$\frac{3}{2000}y^{-0.25}$$