Solve {r}{12,98}{+13,47}{+14,08}{+15,21}{+16,08}{+17,5y}

$$\left. \begin{array} { r } { 12,98 } \\ { + 13,47 } \\ { + 14,08 } \\ { + 15,21 } \\ { + 16,08 } \\ { + 17,5 y } \end{array} \right.$$

Evaluate

$$\frac{35y}{2}+71,82$$

Solution Steps

Add 12,98 and 13,47 to get 26,45.

$$26,45+14,08+15,21+16,08+17,5y$$

Add 26,45 and 14,08 to get 40,53.

$$40,53+15,21+16,08+17,5y$$

Add 40,53 and 15,21 to get 55,74.

$$55,74+16,08+17,5y$$

Add 55,74 and 16,08 to get 71,82.

$$71,82+17,5y$$

Differentiate w.r.t. y

$$17,5$$

Steps Using Derivative Rule for Sum

Add 12,98 and 13,47 to get 26,45.

$$\frac{\mathrm{d}}{\mathrm{d}y}(26,45+14,08+15,21+16,08+17,5y)$$

Add 26,45 and 14,08 to get 40,53.

$$\frac{\mathrm{d}}{\mathrm{d}y}(40,53+15,21+16,08+17,5y)$$

Add 40,53 and 15,21 to get 55,74.

$$\frac{\mathrm{d}}{\mathrm{d}y}(55,74+16,08+17,5y)$$

Add 55,74 and 16,08 to get 71,82.

$$\frac{\mathrm{d}}{\mathrm{d}y}(71,82+17,5y)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$17,5y^{1-1}$$

Subtract 1 from 1.

$$17,5y^{0}$$

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

$$17,5\times 1$$

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

$$17,5$$