Solve 5000div74*1x*10x

$$5000 \div 74 \times 1x \times 10x$$

Evaluate

$$\frac{25000x^{2}}{37}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{5000}{74}\times 1x^{2}\times 10$$

Reduce the fraction \frac{5000}{74} to lowest terms by extracting and canceling out 2.

$$\frac{2500}{37}\times 1x^{2}\times 10$$

Multiply \frac{2500}{37} and 1 to get \frac{2500}{37}.

$$\frac{2500}{37}x^{2}\times 10$$

Express \frac{2500}{37}\times 10 as a single fraction.

$$\frac{2500\times 10}{37}x^{2}$$

Multiply 2500 and 10 to get 25000.

$$\frac{25000}{37}x^{2}$$

Differentiate w.r.t. x

$$\frac{50000x}{37}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5000}{74}\times 1x^{2}\times 10)$$

Reduce the fraction \frac{5000}{74} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2500}{37}\times 1x^{2}\times 10)$$

Multiply \frac{2500}{37} and 1 to get \frac{2500}{37}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2500}{37}x^{2}\times 10)$$

Express \frac{2500}{37}\times 10 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2500\times 10}{37}x^{2})$$

Multiply 2500 and 10 to get 25000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{25000}{37}x^{2})$$

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

$$2\times \frac{25000}{37}x^{2-1}$$

Multiply 2 times \frac{25000}{37}.

$$\frac{50000}{37}x^{2-1}$$

Subtract 1 from 2.

$$\frac{50000}{37}x^{1}$$

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

$$\frac{50000}{37}x$$