Solve 7x^3-9x^2+13x-6

$$7 x ^ { 3 } - 9 x ^ { 2 } + 13 x - 6$$

Differentiate w.r.t. x

$$21x^{2}-18x+13$$

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}.

$$3\times 7x^{3-1}+2\left(-9\right)x^{2-1}+13x^{1-1}$$

Multiply 3 times 7.

$$21x^{3-1}+2\left(-9\right)x^{2-1}+13x^{1-1}$$

Subtract 1 from 3.

$$21x^{2}+2\left(-9\right)x^{2-1}+13x^{1-1}$$

Multiply 2 times -9.

$$21x^{2}-18x^{2-1}+13x^{1-1}$$

Subtract 1 from 2.

$$21x^{2}-18x^{1}+13x^{1-1}$$

Subtract 1 from 1.

$$21x^{2}-18x^{1}+13x^{0}$$

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

$$21x^{2}-18x+13x^{0}$$

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

$$21x^{2}-18x+13\times 1$$

For any term t, t\times 1=t and 1t=t.

$$21x^{2}-18x+13$$

Evaluate

$$7x^{3}-9x^{2}+13x-6$$