Solve 10x^3-11x^4+30x^5+9

$$10 { x }^{ 3 } -11 { x }^{ 4 } +30 { x }^{ 5 } +9$$

Differentiate w.r.t. x

$$2x^{2}\left(75x^{2}-22x+15\right)$$

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}.

$$3\times 10x^{3-1}+4\left(-11\right)x^{4-1}+5\times 30x^{5-1}$$

Multiply 3 times 10.

$$30x^{3-1}+4\left(-11\right)x^{4-1}+5\times 30x^{5-1}$$

Subtract 1 from 3.

$$30x^{2}+4\left(-11\right)x^{4-1}+5\times 30x^{5-1}$$

Multiply 4 times -11.

$$30x^{2}-44x^{4-1}+5\times 30x^{5-1}$$

Subtract 1 from 4.

$$30x^{2}-44x^{3}+5\times 30x^{5-1}$$

Multiply 4 times -11.

$$30x^{2}-44x^{3}+150x^{5-1}$$

Subtract 1 from 5.

$$30x^{2}-44x^{3}+150x^{4}$$

Evaluate

$$30x^{5}-11x^{4}+10x^{3}+9$$