Solve x^2x^3^3

$$x ^ { 2 } x ^ { 3 ^ { 3 } }$$

Evaluate

$$x^{29}$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$x^{2}x^{27}$$

To multiply powers of the same base, add their exponents. Add 2 and 27 to get 29.

$$x^{29}$$

Differentiate w.r.t. x

$$29x^{28}$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 3 and get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{27})$$

To multiply powers of the same base, add their exponents. Add 2 and 27 to get 29.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{29})$$

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

$$29x^{29-1}$$

Subtract 1 from 29.

$$29x^{28}$$