Solve 7-3x^2+5x-3x^7=

$$7 - 3 x ^ { 2 } + 5 x - 3 x ^ { 7 } =$$

Differentiate w.r.t. x

$$5-6x-21x^{6}$$

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}.

$$2\left(-3\right)x^{2-1}+5x^{1-1}+7\left(-3\right)x^{7-1}$$

Multiply 2 times -3.

$$-6x^{2-1}+5x^{1-1}+7\left(-3\right)x^{7-1}$$

Subtract 1 from 2.

$$-6x^{1}+5x^{1-1}+7\left(-3\right)x^{7-1}$$

Subtract 1 from 1.

$$-6x^{1}+5x^{0}+7\left(-3\right)x^{7-1}$$

Multiply 1 times 5.

$$-6x^{1}+5x^{0}-21x^{7-1}$$

Subtract 1 from 7.

$$-6x^{1}+5x^{0}-21x^{6}$$

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

$$-6x+5x^{0}-21x^{6}$$

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

$$-6x+5\times 1-21x^{6}$$

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

$$-6x+5-21x^{6}$$

Evaluate

$$7+5x-3x^{2}-3x^{7}$$