Solve P(x)=2x^5+4x^3-25x^2+21

$$P ( x ) = 2 x ^ { 5 } + 4 x ^ { 3 } - 25 x ^ { 2 } + 21$$

Differentiate w.r.t. x

$$2x\left(5x^{3}+6x-25\right)$$

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}.

$$5\times 2x^{5-1}+3\times 4x^{3-1}+2\left(-25\right)x^{2-1}$$

Multiply 5 times 2.

$$10x^{5-1}+3\times 4x^{3-1}+2\left(-25\right)x^{2-1}$$

Subtract 1 from 5.

$$10x^{4}+3\times 4x^{3-1}+2\left(-25\right)x^{2-1}$$

Multiply 3 times 4.

$$10x^{4}+12x^{3-1}+2\left(-25\right)x^{2-1}$$

Subtract 1 from 3.

$$10x^{4}+12x^{2}+2\left(-25\right)x^{2-1}$$

Multiply 3 times 4.

$$10x^{4}+12x^{2}-50x^{2-1}$$

Subtract 1 from 2.

$$10x^{4}+12x^{2}-50x^{1}$$

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

$$10x^{4}+12x^{2}-50x$$

Evaluate

$$2x^{5}+4x^{3}-25x^{2}+21$$