Solve 2(2/5*y)(1/25y)

$$2 ( \frac { 2 } { 5 } \times y ) ( \frac { 1 } { 25 } y )$$

Evaluate

$$\frac{4y^{2}}{125}$$

Solution Steps

Multiply y and y to get y^{2}.

$$2\times \frac{2}{5}y^{2}\times \frac{1}{25}$$

Express 2\times \frac{2}{5} as a single fraction.

$$\frac{2\times 2}{5}y^{2}\times \frac{1}{25}$$

Multiply 2 and 2 to get 4.

$$\frac{4}{5}y^{2}\times \frac{1}{25}$$

Multiply \frac{4}{5} times \frac{1}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 1}{5\times 25}y^{2}$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 25}.

$$\frac{4}{125}y^{2}$$

Differentiate w.r.t. y

$$\frac{8y}{125}$$

Steps Using Definition of a Derivative

Multiply y and y to get y^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2\times \frac{2}{5}y^{2}\times \frac{1}{25})$$

Express 2\times \frac{2}{5} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2\times 2}{5}y^{2}\times \frac{1}{25})$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4}{5}y^{2}\times \frac{1}{25})$$

Multiply \frac{4}{5} times \frac{1}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4\times 1}{5\times 25}y^{2})$$

Do the multiplications in the fraction \frac{4\times 1}{5\times 25}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4}{125}y^{2})$$

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

$$2\times \frac{4}{125}y^{2-1}$$

Multiply 2 times \frac{4}{125}.

$$\frac{8}{125}y^{2-1}$$

Subtract 1 from 2.

$$\frac{8}{125}y^{1}$$

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

$$\frac{8}{125}y$$