Solve 10ydiv5^2+26ydiv40

$$10 y \div 5 ^ { 2 } + 26 y \div 40$$

Evaluate

$$\frac{21y}{20}$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$\frac{10y}{25}+\frac{26y}{40}$$

Divide 10y by 25 to get \frac{2}{5}y.

$$\frac{2}{5}y+\frac{26y}{40}$$

Divide 26y by 40 to get \frac{13}{20}y.

$$\frac{2}{5}y+\frac{13}{20}y$$

Combine \frac{2}{5}y and \frac{13}{20}y to get \frac{21}{20}y.

$$\frac{21}{20}y$$

Differentiate w.r.t. y

$$\frac{21}{20} = 1\frac{1}{20} = 1.05$$

Steps Using Definition of a Derivative

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{10y}{25}+\frac{26y}{40})$$

Divide 10y by 25 to get \frac{2}{5}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2}{5}y+\frac{26y}{40})$$

Divide 26y by 40 to get \frac{13}{20}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2}{5}y+\frac{13}{20}y)$$

Combine \frac{2}{5}y and \frac{13}{20}y to get \frac{21}{20}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{21}{20}y)$$

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

$$\frac{21}{20}y^{1-1}$$

Subtract 1 from 1.

$$\frac{21}{20}y^{0}$$

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

$$\frac{21}{20}\times 1$$

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

$$\frac{21}{20}$$