Solve 1/2x^200*20^2

$$\frac { 1 } { 2 } x ^ { 200 } \times 20 ^ { 2 }$$

Evaluate

$$200x^{200}$$

Solution Steps

Calculate 20 to the power of 2 and get 400.

$$\frac{1}{2}x^{200}\times 400$$

Multiply \frac{1}{2} and 400 to get 200.

$$200x^{200}$$

Differentiate w.r.t. x

$$40000x^{199}$$

Steps Using Definition of a Derivative

Calculate 20 to the power of 2 and get 400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}x^{200}\times 400)$$

Multiply \frac{1}{2} and 400 to get 200.

$$\frac{\mathrm{d}}{\mathrm{d}x}(200x^{200})$$

The derivative of ax^{n} is nax^{n-1}.

$$200\times 200x^{200-1}$$

Multiply 200 times 200.

$$40000x^{200-1}$$

Subtract 1 from 200.

$$40000x^{199}$$