Solve x-9*x^2+7x-3

$$x-9 \times { x }^{ 2 } +7x-3$$

Differentiate w.r.t. x

$$8-18x$$

Steps Using Derivative Rule for Sum

Combine x and 7x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x-9x^{2}-3)$$

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}.

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

Subtract 1 from 1.

$$8x^{0}+2\left(-9\right)x^{2-1}$$

Multiply 2 times -9.

$$8x^{0}-18x^{2-1}$$

Subtract 1 from 2.

$$8x^{0}-18x^{1}$$

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

$$8x^{0}-18x$$

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

$$8\times 1-18x$$

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

$$8-18x$$

Evaluate

$$-9x^{2}+8x-3$$

Solution Steps

Combine x and 7x to get 8x.

$$8x-9x^{2}-3$$