Solve -6x^5-8x^2+9x-7

$$- 6 x ^ { 5 } - 8 x ^ { 2 } + 9 x - 7$$

Differentiate w.r.t. x

$$9-16x-30x^{4}$$

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}.

$$5\left(-6\right)x^{5-1}+2\left(-8\right)x^{2-1}+9x^{1-1}$$

Multiply 5 times -6.

$$-30x^{5-1}+2\left(-8\right)x^{2-1}+9x^{1-1}$$

Subtract 1 from 5.

$$-30x^{4}+2\left(-8\right)x^{2-1}+9x^{1-1}$$

Multiply 2 times -8.

$$-30x^{4}-16x^{2-1}+9x^{1-1}$$

Subtract 1 from 2.

$$-30x^{4}-16x^{1}+9x^{1-1}$$

Subtract 1 from 1.

$$-30x^{4}-16x^{1}+9x^{0}$$

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

$$-30x^{4}-16x+9x^{0}$$

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

$$-30x^{4}-16x+9\times 1$$

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

$$-30x^{4}-16x+9$$

Evaluate

$$-6x^{5}-8x^{2}+9x-7$$