Solve 2-x-9(0)+3x^2+x+4(-9)

$$2 - x - 9 ( 0 ) + 3 x ^ { 2 } + x + 4 ( - 9 )$$

Evaluate

$$3x^{2}-34$$

Solution Steps

Multiply 9 and 0 to get 0.

$$2-x-0+3x^{2}+x+4\left(-9\right)$$

Multiply 4 and -9 to get -36.

$$2-x-0+3x^{2}+x-36$$

Multiply -1 and 0 to get 0.

$$2-x+0+3x^{2}+x-36$$

Add 2 and 0 to get 2.

$$2-x+3x^{2}+x-36$$

Combine -x and x to get 0.

$$2+3x^{2}-36$$

Subtract 36 from 2 to get -34.

$$-34+3x^{2}$$

Differentiate w.r.t. x

$$6x$$

Steps Using Derivative Rule for Sum

Multiply 9 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2-x-0+3x^{2}+x+4\left(-9\right))$$

Multiply 4 and -9 to get -36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2-x-0+3x^{2}+x-36)$$

Multiply -1 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2-x+0+3x^{2}+x-36)$$

Add 2 and 0 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2-x+3x^{2}+x-36)$$

Combine -x and x to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2+3x^{2}-36)$$

Subtract 36 from 2 to get -34.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-34+3x^{2})$$

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}.

$$2\times 3x^{2-1}$$

Multiply 2 times 3.

$$6x^{2-1}$$

Subtract 1 from 2.

$$6x^{1}$$

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

$$6x$$