Solve 8x^3+3x-1x^2-2x+38x^3-1

$$8 x ^ { 3 } + 3 x - 1 x ^ { 2 } - 2 x + 38 x ^ { 3 } - 1$$

Evaluate

$$46x^{3}-x^{2}+x-1$$

Solution Steps

Combine 3x and -2x to get x.

$$8x^{3}+x-x^{2}+38x^{3}-1$$

Combine 8x^{3} and 38x^{3} to get 46x^{3}.

$$46x^{3}+x-x^{2}-1$$

Differentiate w.r.t. x

$$138x^{2}-2x+1$$

Steps Using Derivative Rule for Sum

Combine 3x and -2x to get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{3}+x-x^{2}+38x^{3}-1)$$

Combine 8x^{3} and 38x^{3} to get 46x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(46x^{3}+x-x^{2}-1)$$

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}.

$$3\times 46x^{3-1}+x^{1-1}+2\left(-1\right)x^{2-1}$$

Multiply 3 times 46.

$$138x^{3-1}+x^{1-1}+2\left(-1\right)x^{2-1}$$

Subtract 1 from 3.

$$138x^{2}+x^{1-1}+2\left(-1\right)x^{2-1}$$

Subtract 1 from 1.

$$138x^{2}+x^{0}+2\left(-1\right)x^{2-1}$$

Multiply 1 times 1.

$$138x^{2}+x^{0}-2x^{2-1}$$

Subtract 1 from 2.

$$138x^{2}+x^{0}-2x^{1}$$

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

$$138x^{2}+x^{0}-2x$$

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

$$138x^{2}+1-2x$$