Solve (7a^3-2a-2)+(-5a+3)

$$( 7 a ^ { 3 } - 2 a - 2 ) + ( - 5 a + 3 )$$

Evaluate

$$7a^{3}-7a+1$$

Solution Steps

Combine -2a and -5a to get -7a.

$$7a^{3}-7a-2+3$$

Add -2 and 3 to get 1.

$$7a^{3}-7a+1$$

Differentiate w.r.t. a

$$21a^{2}-7$$

Steps Using Derivative Rule for Sum

Combine -2a and -5a to get -7a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a^{3}-7a-2+3)$$

Add -2 and 3 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7a^{3}-7a+1)$$

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}.

$$3\times 7a^{3-1}-7a^{1-1}$$

Multiply 3 times 7.

$$21a^{3-1}-7a^{1-1}$$

Subtract 1 from 3.

$$21a^{2}-7a^{1-1}$$

Subtract 1 from 1.

$$21a^{2}-7a^{0}$$

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

$$21a^{2}-7$$