Solve =30x^5-8x^3+9x^2-1

$$= 30 x ^ { 5 } - 8 x ^ { 3 } + 9 x ^ { 2 } - 1$$

Differentiate w.r.t. x

$$6x\left(25x^{3}-4x+3\right)$$

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}.

$$5\times 30x^{5-1}+3\left(-8\right)x^{3-1}+2\times 9x^{2-1}$$

Multiply 5 times 30.

$$150x^{5-1}+3\left(-8\right)x^{3-1}+2\times 9x^{2-1}$$

Subtract 1 from 5.

$$150x^{4}+3\left(-8\right)x^{3-1}+2\times 9x^{2-1}$$

Multiply 3 times -8.

$$150x^{4}-24x^{3-1}+2\times 9x^{2-1}$$

Subtract 1 from 3.

$$150x^{4}-24x^{2}+2\times 9x^{2-1}$$

Multiply 3 times -8.

$$150x^{4}-24x^{2}+18x^{2-1}$$

Subtract 1 from 2.

$$150x^{4}-24x^{2}+18x^{1}$$

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

$$150x^{4}-24x^{2}+18x$$

Evaluate

$$30x^{5}-8x^{3}+9x^{2}-1$$