Solve (x^3-6x^2+4)+(10x^3-2x^2-20)

$$( x ^ { 3 } - 6 x ^ { 2 } + 4 ) + ( 10 x ^ { 3 } - 2 x ^ { 2 } - 20 )$$

Evaluate

$$11x^{3}-8x^{2}-16$$

Solution Steps

Combine x^{3} and 10x^{3} to get 11x^{3}.

$$11x^{3}-6x^{2}+4-2x^{2}-20$$

Combine -6x^{2} and -2x^{2} to get -8x^{2}.

$$11x^{3}-8x^{2}+4-20$$

Subtract 20 from 4 to get -16.

$$11x^{3}-8x^{2}-16$$

Differentiate w.r.t. x

$$x\left(33x-16\right)$$

Steps Using Derivative Rule for Sum

Combine x^{3} and 10x^{3} to get 11x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}-6x^{2}+4-2x^{2}-20)$$

Combine -6x^{2} and -2x^{2} to get -8x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}-8x^{2}+4-20)$$

Subtract 20 from 4 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}-8x^{2}-16)$$

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}.

$$3\times 11x^{3-1}+2\left(-8\right)x^{2-1}$$

Multiply 3 times 11.

$$33x^{3-1}+2\left(-8\right)x^{2-1}$$

Subtract 1 from 3.

$$33x^{2}+2\left(-8\right)x^{2-1}$$

Multiply 2 times -8.

$$33x^{2}-16x^{2-1}$$

Subtract 1 from 2.

$$33x^{2}-16x^{1}$$

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

$$33x^{2}-16x$$