Solve x^2-3+25:1/2dx

$$x ^ { 2 } - 3 + 25 : \frac { 1 } { 2 } d x$$

Evaluate

$$x^{2}+50dx-3$$

Solution Steps

Divide 25 by \frac{1}{2} by multiplying 25 by the reciprocal of \frac{1}{2}.

$$x^{2}-3+25\times 2dx$$

Multiply 25 and 2 to get 50.

$$x^{2}-3+50dx$$

Differentiate w.r.t. x

$$2\left(x+25d\right)$$

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}.

$$2x^{2-1}+50dx^{1-1}$$

Subtract 1 from 2.

$$2x^{1}+50dx^{1-1}$$

Subtract 1 from 1.

$$2x^{1}+50dx^{0}$$

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

$$2x+50dx^{0}$$

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

$$2x+50d\times 1$$

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

$$2x+50d$$