Solve x^16/2^1-5^2

$$\frac { x ^ { 16 } } { 2 ^ { 1 } - 5 ^ { 2 } }$$

Evaluate

$$-\frac{x^{16}}{23}$$

Solution Steps

Calculate 2 to the power of 1 and get 2.

$$\frac{x^{16}}{2-5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{x^{16}}{2-25}$$

Subtract 25 from 2 to get -23.

$$\frac{x^{16}}{-23}$$

Differentiate w.r.t. x

$$-\frac{16x^{15}}{23}$$

Steps Using Definition of a Derivative

Calculate 2 to the power of 1 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{16}}{2-5^{2}})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{16}}{2-25})$$

Subtract 25 from 2 to get -23.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{16}}{-23})$$

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

$$16\left(-\frac{1}{23}\right)x^{16-1}$$

Multiply 16 times -\frac{1}{23}.

$$-\frac{16}{23}x^{16-1}$$

Subtract 1 from 16.

$$-\frac{16}{23}x^{15}$$