Solve -x^2x+x+3x^2-7+11

$$- { x }^{ 2 } x+x+3 { x }^{ 2 } -7+11$$

Evaluate

$$4+x+3x^{2}-x^{3}$$

Solution Steps

Add -7 and 11 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-x^{3}+x+3x^{2}+4$$

Differentiate w.r.t. x

$$1+6x-3x^{2}$$

Steps Using Derivative Rule for Sum

Add -7 and 11 to get 4.

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

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}.

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

Multiply 3 times -1.

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

Subtract 1 from 3.

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

Subtract 1 from 1.

$$-3x^{2}+x^{0}+2\times 3x^{2-1}$$

Multiply 1 times 1.

$$-3x^{2}+x^{0}+6x^{2-1}$$

Subtract 1 from 2.

$$-3x^{2}+x^{0}+6x^{1}$$

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

$$-3x^{2}+x^{0}+6x$$

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

$$-3x^{2}+1+6x$$