Solve 2x^2left(6^2right)^2

$$2 { x }^{ 2 } { \left( { 6 }^{ 2 } \right) }^{ 2 }$$

Evaluate

$$2592x^{2}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2x^{2}\times 6^{4}$$

Calculate 6 to the power of 4 and get 1296.

$$2x^{2}\times 1296$$

Multiply 2 and 1296 to get 2592.

$$2592x^{2}$$

Differentiate w.r.t. x

$$5184x$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}\times 6^{4})$$

Calculate 6 to the power of 4 and get 1296.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}\times 1296)$$

Multiply 2 and 1296 to get 2592.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2592x^{2})$$

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

$$2\times 2592x^{2-1}$$

Multiply 2 times 2592.

$$5184x^{2-1}$$

Subtract 1 from 2.

$$5184x^{1}$$

For any term t, t^{1}=t.

$$5184x$$