Solve 4x^{4}+2x^{2}-3x^7+2)-(3x^9+4x^8+4x^7-1)

$$4 x ^ { 4 } + 2 x ^ { 2 } - 3 x ^ { 7 } + 2 ) - ( 3 x ^ { 9 } + 4 x ^ { 8 } + 4 x ^ { 7 } - 1 )$$

Differentiate w.r.t. x

$$x\left(4+16x^{2}-21x^{5}\right)$$

Steps Using Derivative Rule for Sum

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}.

$$4\times 4x^{4-1}+2\times 2x^{2-1}+7\left(-3\right)x^{7-1}$$

Multiply 4 times 4.

$$16x^{4-1}+2\times 2x^{2-1}+7\left(-3\right)x^{7-1}$$

Subtract 1 from 4.

$$16x^{3}+2\times 2x^{2-1}+7\left(-3\right)x^{7-1}$$

Multiply 2 times 2.

$$16x^{3}+4x^{2-1}+7\left(-3\right)x^{7-1}$$

Subtract 1 from 2.

$$16x^{3}+4x^{1}+7\left(-3\right)x^{7-1}$$

Multiply 2 times 2.

$$16x^{3}+4x^{1}-21x^{7-1}$$

Subtract 1 from 7.

$$16x^{3}+4x^{1}-21x^{6}$$

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

$$16x^{3}+4x-21x^{6}$$

Evaluate

$$2+2x^{2}+4x^{4}-3x^{7}$$