Solve (3t^2-2t-1)+(4t^2-7t+6)

$$( 3 t ^ { 2 } - 2 t - 1 ) + ( 4 t ^ { 2 } - 7 t + 6 )$$

Evaluate

$$7t^{2}-9t+5$$

Solution Steps

Combine 3t^{2} and 4t^{2} to get 7t^{2}.

$$7t^{2}-2t-1-7t+6$$

Combine -2t and -7t to get -9t.

$$7t^{2}-9t-1+6$$

Add -1 and 6 to get 5.

$$7t^{2}-9t+5$$

Differentiate w.r.t. t

$$14t-9$$

Steps Using Derivative Rule for Sum

Combine 3t^{2} and 4t^{2} to get 7t^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(7t^{2}-2t-1-7t+6)$$

Combine -2t and -7t to get -9t.

$$\frac{\mathrm{d}}{\mathrm{d}t}(7t^{2}-9t-1+6)$$

Add -1 and 6 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}t}(7t^{2}-9t+5)$$

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}.

$$2\times 7t^{2-1}-9t^{1-1}$$

Multiply 2 times 7.

$$14t^{2-1}-9t^{1-1}$$

Subtract 1 from 2.

$$14t^{1}-9t^{1-1}$$

Subtract 1 from 1.

$$14t^{1}-9t^{0}$$

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

$$14t-9t^{0}$$

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

$$14t-9$$