Solve 35c^3+40c^2-14

$$35 c ^ { 3 } + 40 c ^ { 2 } - 14$$

Differentiate w.r.t. c

$$5c\left(21c+16\right)$$

Steps Using Derivative Rule for Sum

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}.

$$3\times 35c^{3-1}+2\times 40c^{2-1}$$

Multiply 3 times 35.

$$105c^{3-1}+2\times 40c^{2-1}$$

Subtract 1 from 3.

$$105c^{2}+2\times 40c^{2-1}$$

Multiply 2 times 40.

$$105c^{2}+80c^{2-1}$$

Subtract 1 from 2.

$$105c^{2}+80c^{1}$$

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

$$105c^{2}+80c$$

Evaluate

$$35c^{3}+40c^{2}-14$$