Solve x^2-10x^2+6x-7-5x

$$x ^ { 2 } - 10 x ^ { 2 } + 6 x - 7 - 5 x$$

Evaluate

$$-9x^{2}+x-7$$

Solution Steps

Combine x^{2} and -10x^{2} to get -9x^{2}.

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

Combine 6x and -5x to get x.

$$-9x^{2}+x-7$$

Differentiate w.r.t. x

$$1-18x$$

Steps Using Derivative Rule for Sum

Combine x^{2} and -10x^{2} to get -9x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-9x^{2}+6x-7-5x)$$

Combine 6x and -5x to get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-9x^{2}+x-7)$$

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}.

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

Multiply 2 times -9.

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

Subtract 1 from 2.

$$-18x^{1}+x^{1-1}$$

Subtract 1 from 1.

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

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

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

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

$$-18x+1$$