Solve 2619*2430*9999^2/x

$$2619 \cdot 2430 \cdot \frac{ { 9999 }^{ 2 } }{ x }$$

Evaluate

$$\frac{636289722964170}{x}$$

Solution Steps

Multiply 2619 and 2430 to get 6364170.

$$6364170\times \frac{9999^{2}}{x}$$

Calculate 9999 to the power of 2 and get 99980001.

$$6364170\times \frac{99980001}{x}$$

Express 6364170\times \frac{99980001}{x} as a single fraction.

$$\frac{6364170\times 99980001}{x}$$

Multiply 6364170 and 99980001 to get 636289722964170.

$$\frac{636289722964170}{x}$$

Differentiate w.r.t. x

$$-\frac{636289722964170}{x^{2}}$$

Steps Using Definition of a Derivative

Multiply 2619 and 2430 to get 6364170.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6364170\times \frac{9999^{2}}{x})$$

Calculate 9999 to the power of 2 and get 99980001.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6364170\times \frac{99980001}{x})$$

Express 6364170\times \frac{99980001}{x} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6364170\times 99980001}{x})$$

Multiply 6364170 and 99980001 to get 636289722964170.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{636289722964170}{x})$$

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

$$-636289722964170x^{-1-1}$$

Subtract 1 from -1.

$$-636289722964170x^{-2}$$