Solve (5x^2-3x+4)+(8x^3-8x)

$$( 5 x ^ { 2 } - 3 x + 4 ) + ( 8 x ^ { 3 } - 8 x )$$

Differentiate w.r.t. x

$$\left(2x-1\right)\left(12x+11\right)$$

Steps Using Derivative Rule for Sum

Combine -3x and -8x to get -11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-11x+4+8x^{3})$$

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}.

$$2\times 5x^{2-1}-11x^{1-1}+3\times 8x^{3-1}$$

Multiply 2 times 5.

$$10x^{2-1}-11x^{1-1}+3\times 8x^{3-1}$$

Subtract 1 from 2.

$$10x^{1}-11x^{1-1}+3\times 8x^{3-1}$$

Subtract 1 from 1.

$$10x^{1}-11x^{0}+3\times 8x^{3-1}$$

Multiply 1 times -11.

$$10x^{1}-11x^{0}+24x^{3-1}$$

Subtract 1 from 3.

$$10x^{1}-11x^{0}+24x^{2}$$

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

$$10x-11x^{0}+24x^{2}$$

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

$$10x-11+24x^{2}$$

Evaluate

$$8x^{3}+5x^{2}-11x+4$$

Solution Steps

Combine -3x and -8x to get -11x.

$$5x^{2}-11x+4+8x^{3}$$