Solve 5*100y3/29y=

$$5 \cdot 100 y \frac { 3 } { 2 } 9 y =$$

Evaluate

$$6750y^{2}$$

Solution Steps

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

$$5\times 100y^{2}\times \frac{3}{2}\times 9$$

Multiply 5 and 100 to get 500.

$$500y^{2}\times \frac{3}{2}\times 9$$

Express 500\times \frac{3}{2} as a single fraction.

$$\frac{500\times 3}{2}y^{2}\times 9$$

Multiply 500 and 3 to get 1500.

$$\frac{1500}{2}y^{2}\times 9$$

Divide 1500 by 2 to get 750.

$$750y^{2}\times 9$$

Multiply 750 and 9 to get 6750.

$$6750y^{2}$$

Differentiate w.r.t. y

$$13500y$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(5\times 100y^{2}\times \frac{3}{2}\times 9)$$

Multiply 5 and 100 to get 500.

$$\frac{\mathrm{d}}{\mathrm{d}y}(500y^{2}\times \frac{3}{2}\times 9)$$

Express 500\times \frac{3}{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{500\times 3}{2}y^{2}\times 9)$$

Multiply 500 and 3 to get 1500.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{1500}{2}y^{2}\times 9)$$

Divide 1500 by 2 to get 750.

$$\frac{\mathrm{d}}{\mathrm{d}y}(750y^{2}\times 9)$$

Multiply 750 and 9 to get 6750.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6750y^{2})$$

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

$$2\times 6750y^{2-1}$$

Multiply 2 times 6750.

$$13500y^{2-1}$$

Subtract 1 from 2.

$$13500y^{1}$$

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

$$13500y$$