Solve (36x^3-13x-3)+(6x-5)

$$( 36 x ^ { 3 } - 13 x - 3 ) + ( 6 x - 5 )$$

Evaluate

$$36x^{3}-7x-8$$

Solution Steps

Combine -13x and 6x to get -7x.

$$36x^{3}-7x-3-5$$

Subtract 5 from -3 to get -8.

$$36x^{3}-7x-8$$

Differentiate w.r.t. x

$$108x^{2}-7$$

Steps Using Derivative Rule for Sum

Combine -13x and 6x to get -7x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{3}-7x-3-5)$$

Subtract 5 from -3 to get -8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{3}-7x-8)$$

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}.

$$3\times 36x^{3-1}-7x^{1-1}$$

Multiply 3 times 36.

$$108x^{3-1}-7x^{1-1}$$

Subtract 1 from 3.

$$108x^{2}-7x^{1-1}$$

Subtract 1 from 1.

$$108x^{2}-7x^{0}$$

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

$$108x^{2}-7$$