Solve 51^2left(x^2right)^2

$${ 51 }^{ 2 } { \left( { x }^{ 2 } \right) }^{ 2 }$$

Evaluate

$$2601x^{4}$$

Solution Steps

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

$$51^{2}x^{4}$$

Calculate 51 to the power of 2 and get 2601.

$$2601x^{4}$$

Differentiate w.r.t. x

$$10404x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(51^{2}x^{4})$$

Calculate 51 to the power of 2 and get 2601.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2601x^{4})$$

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

$$4\times 2601x^{4-1}$$

Multiply 4 times 2601.

$$10404x^{4-1}$$

Subtract 1 from 4.

$$10404x^{3}$$