Solve 5-7x^2+x^3+2

$$5 - 7 x ^ { 2 } + x ^ { 3 } + 2$$

Differentiate w.r.t. x

$$x\left(3x-14\right)$$

Steps Using Derivative Rule for Sum

Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7-7x^{2}+x^{3})$$

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}.

$$2\left(-7\right)x^{2-1}+3x^{3-1}$$

Multiply 2 times -7.

$$-14x^{2-1}+3x^{3-1}$$

Subtract 1 from 2.

$$-14x^{1}+3x^{3-1}$$

Subtract 1 from 3.

$$-14x^{1}+3x^{2}$$

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

$$-14x+3x^{2}$$

Evaluate

$$x^{3}-7x^{2}+7$$

Solution Steps

Add 5 and 2 to get 7.

$$7-7x^{2}+x^{3}$$