Solve 48x^9-8x^7+x^3-48

$$48 { x }^{ 9 } -8 { x }^{ 7 } + { x }^{ 3 } -48$$

Differentiate w.r.t. x

$$x^{2}\left(432x^{6}-56x^{4}+3\right)$$

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}.

$$9\times 48x^{9-1}+7\left(-8\right)x^{7-1}+3x^{3-1}$$

Multiply 9 times 48.

$$432x^{9-1}+7\left(-8\right)x^{7-1}+3x^{3-1}$$

Subtract 1 from 9.

$$432x^{8}+7\left(-8\right)x^{7-1}+3x^{3-1}$$

Multiply 7 times -8.

$$432x^{8}-56x^{7-1}+3x^{3-1}$$

Subtract 1 from 7.

$$432x^{8}-56x^{6}+3x^{3-1}$$

Subtract 1 from 3.

$$432x^{8}-56x^{6}+3x^{2}$$

Evaluate

$$48x^{9}-8x^{7}+x^{3}-48$$