Solve 3y/6y*10y=

$$3 y / 6 y \times 10 y =$$

Evaluate

$$5y^{3}$$

Solution Steps

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

$$\frac{3y}{6}y^{2}\times 10$$

Divide 3y by 6 to get \frac{1}{2}y.

$$\frac{1}{2}yy^{2}\times 10$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{1}{2}y^{3}\times 10$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$\frac{10}{2}y^{3}$$

Divide 10 by 2 to get 5.

$$5y^{3}$$

Differentiate w.r.t. y

$$15y^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3y}{6}y^{2}\times 10)$$

Divide 3y by 6 to get \frac{1}{2}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{2}yy^{2}\times 10)$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1}{2}y^{3}\times 10)$$

Multiply \frac{1}{2} and 10 to get \frac{10}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{10}{2}y^{3})$$

Divide 10 by 2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{3})$$

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

$$3\times 5y^{3-1}$$

Multiply 3 times 5.

$$15y^{3-1}$$

Subtract 1 from 3.

$$15y^{2}$$