Solve x^3-2x^2+x-3quadx^2+1

$$x ^ { 3 } - 2 x ^ { 2 } + x - 3 \quad x ^ { 2 } + 1$$

Differentiate w.r.t. x

$$3x^{2}-10x+1$$

Steps Using Derivative Rule for Sum

Combine -2x^{2} and -3x^{2} to get -5x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}-5x^{2}+x+1)$$

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}.

$$3x^{3-1}+2\left(-5\right)x^{2-1}+x^{1-1}$$

Subtract 1 from 3.

$$3x^{2}+2\left(-5\right)x^{2-1}+x^{1-1}$$

Multiply 2 times -5.

$$3x^{2}-10x^{2-1}+x^{1-1}$$

Subtract 1 from 2.

$$3x^{2}-10x^{1}+x^{1-1}$$

Subtract 1 from 1.

$$3x^{2}-10x^{1}+x^{0}$$

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

$$3x^{2}-10x+x^{0}$$

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

$$3x^{2}-10x+1$$

Evaluate

$$x^{3}-5x^{2}+x+1$$

Solution Steps

Combine -2x^{2} and -3x^{2} to get -5x^{2}.

$$x^{3}-5x^{2}+x+1$$