Solve a*(+15)+(-14)+(+19)+(-6)

$$a \cdot ( + 15 ) + ( - 14 ) + ( + 19 ) + ( - 6 )$$

Evaluate

$$15a-1$$

Solution Steps

Add -14 and 19 to get 5.

$$a\times 15+5-6$$

Subtract 6 from 5 to get -1.

$$a\times 15-1$$

Differentiate w.r.t. a

$$15$$

Steps Using Derivative Rule for Sum

Add -14 and 19 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times 15+5-6)$$

Subtract 6 from 5 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times 15-1)$$

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}.

$$15a^{1-1}$$

Subtract 1 from 1.

$$15a^{0}$$

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

$$15\times 1$$

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

$$15$$