Solve (9x^2-9x+1)+(7x^3-9x)

$$( 9 x ^ { 2 } - 9 x + 1 ) + ( 7 x ^ { 3 } - 9 x )$$

Differentiate w.r.t. x

$$21x^{2}+18x-18$$

Steps Using Derivative Rule for Sum

Combine -9x and -9x to get -18x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}-18x+1+7x^{3})$$

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}.

$$2\times 9x^{2-1}-18x^{1-1}+3\times 7x^{3-1}$$

Multiply 2 times 9.

$$18x^{2-1}-18x^{1-1}+3\times 7x^{3-1}$$

Subtract 1 from 2.

$$18x^{1}-18x^{1-1}+3\times 7x^{3-1}$$

Subtract 1 from 1.

$$18x^{1}-18x^{0}+3\times 7x^{3-1}$$

Multiply 1 times -18.

$$18x^{1}-18x^{0}+21x^{3-1}$$

Subtract 1 from 3.

$$18x^{1}-18x^{0}+21x^{2}$$

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

$$18x-18x^{0}+21x^{2}$$

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

$$18x-18+21x^{2}$$

Evaluate

$$7x^{3}+9x^{2}-18x+1$$

Solution Steps

Combine -9x and -9x to get -18x.

$$9x^{2}-18x+1+7x^{3}$$