Solve (7t^2+9)+(6t^2+8)

$$( 7 t ^ { 2 } + 9 ) + ( 6 t ^ { 2 } + 8 )$$

Evaluate

$$13t^{2}+17$$

Solution Steps

Combine 7t^{2} and 6t^{2} to get 13t^{2}.

$$13t^{2}+9+8$$

Add 9 and 8 to get 17.

$$13t^{2}+17$$

Differentiate w.r.t. t

$$26t$$

Steps Using Derivative Rule for Sum

Combine 7t^{2} and 6t^{2} to get 13t^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(13t^{2}+9+8)$$

Add 9 and 8 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}t}(13t^{2}+17)$$

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}.

$$2\times 13t^{2-1}$$

Multiply 2 times 13.

$$26t^{2-1}$$

Subtract 1 from 2.

$$26t^{1}$$

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

$$26t$$