Solve f(x)=25x^4-7x^3+2x+10

$$f ( x ) = 25 x ^ { 4 } - 7 x ^ { 3 } + 2 x + 10$$

Differentiate w.r.t. x

$$100x^{3}-21x^{2}+2$$

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}.

$$4\times 25x^{4-1}+3\left(-7\right)x^{3-1}+2x^{1-1}$$

Multiply 4 times 25.

$$100x^{4-1}+3\left(-7\right)x^{3-1}+2x^{1-1}$$

Subtract 1 from 4.

$$100x^{3}+3\left(-7\right)x^{3-1}+2x^{1-1}$$

Multiply 3 times -7.

$$100x^{3}-21x^{3-1}+2x^{1-1}$$

Subtract 1 from 3.

$$100x^{3}-21x^{2}+2x^{1-1}$$

Subtract 1 from 1.

$$100x^{3}-21x^{2}+2x^{0}$$

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

$$100x^{3}-21x^{2}+2\times 1$$

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

$$100x^{3}-21x^{2}+2$$

Evaluate

$$25x^{4}-7x^{3}+2x+10$$