Solve (4x-x^3+8)+(-2x^3+3x^2)=

$$( 4 x - x ^ { 3 } + 8 ) + ( - 2 x ^ { 3 } + 3 x ^ { 2 } ) =$$

Differentiate w.r.t. x

$$4+6x-9x^{2}$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x-3x^{3}+8+3x^{2})$$

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}.

$$4x^{1-1}+3\left(-3\right)x^{3-1}+2\times 3x^{2-1}$$

Subtract 1 from 1.

$$4x^{0}+3\left(-3\right)x^{3-1}+2\times 3x^{2-1}$$

Multiply 3 times -3.

$$4x^{0}-9x^{3-1}+2\times 3x^{2-1}$$

Subtract 1 from 3.

$$4x^{0}-9x^{2}+2\times 3x^{2-1}$$

Multiply 3 times -3.

$$4x^{0}-9x^{2}+6x^{2-1}$$

Subtract 1 from 2.

$$4x^{0}-9x^{2}+6x^{1}$$

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

$$4x^{0}-9x^{2}+6x$$

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

$$4\times 1-9x^{2}+6x$$

For any term t, t\times 1=t and 1t=t.

$$4-9x^{2}+6x$$

Evaluate

$$8+4x+3x^{2}-3x^{3}$$

Solution Steps

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

$$4x-3x^{3}+8+3x^{2}$$