Solve frac{3^{5}x^10^5*25}{5^7*6^5}

$$\frac { 3 ^ { 5 } x ^ { 10 ^ { 5 } } \times 25 } { 5 ^ { 7 } \times 6 ^ { 5 } }$$

Evaluate

$$\frac{x^{100000}}{100000}$$

Solution Steps

Calculate 3 to the power of 5 and get 243.

$$\frac{243x^{10^{5}}\times 25}{5^{7}\times 6^{5}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{243x^{100000}\times 25}{5^{7}\times 6^{5}}$$

Multiply 243 and 25 to get 6075.

$$\frac{6075x^{100000}}{5^{7}\times 6^{5}}$$

Calculate 5 to the power of 7 and get 78125.

$$\frac{6075x^{100000}}{78125\times 6^{5}}$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{6075x^{100000}}{78125\times 7776}$$

Multiply 78125 and 7776 to get 607500000.

$$\frac{6075x^{100000}}{607500000}$$

Divide 6075x^{100000} by 607500000 to get \frac{1}{100000}x^{100000}.

$$\frac{1}{100000}x^{100000}$$

Differentiate w.r.t. x

$$x^{99999}$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 5 and get 243.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{243x^{10^{5}}\times 25}{5^{7}\times 6^{5}})$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{243x^{100000}\times 25}{5^{7}\times 6^{5}})$$

Multiply 243 and 25 to get 6075.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6075x^{100000}}{5^{7}\times 6^{5}})$$

Calculate 5 to the power of 7 and get 78125.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6075x^{100000}}{78125\times 6^{5}})$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6075x^{100000}}{78125\times 7776})$$

Multiply 78125 and 7776 to get 607500000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6075x^{100000}}{607500000})$$

Divide 6075x^{100000} by 607500000 to get \frac{1}{100000}x^{100000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{100000}x^{100000})$$

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

$$100000\times \frac{1}{100000}x^{100000-1}$$

Multiply 100000 times \frac{1}{100000}.

$$x^{100000-1}$$

Subtract 1 from 100000.

$$x^{99999}$$