Solve x^333333frac{3{3}}

$$x ^ { 333333 \frac { 3 } { 3 } }$$

Evaluate

$$x^{333334}$$

Solution Steps

Multiply 333333 and 3 to get 999999.

$$x^{\frac{999999+3}{3}}$$

Add 999999 and 3 to get 1000002.

$$x^{\frac{1000002}{3}}$$

Divide 1000002 by 3 to get 333334.

$$x^{333334}$$

Differentiate w.r.t. x

$$333334x^{333333}$$

Steps Using Definition of a Derivative

Multiply 333333 and 3 to get 999999.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{999999+3}{3}})$$

Add 999999 and 3 to get 1000002.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{1000002}{3}})$$

Divide 1000002 by 3 to get 333334.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{333334})$$

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

$$333334x^{333334-1}$$

Subtract 1 from 333334.

$$333334x^{333333}$$