Solve left(x^2right)^2+25^2

$${ \left( { x }^{ 2 } \right) }^{ 2+ { 25 }^{ 2 } }$$

Evaluate

$$x^{1254}$$

Steps for Raising Power to Another Power

Calculate 25 to the power of 2 and get 625.

$$\left(x^{2}\right)^{2+625}$$

Add 2 and 625 to get 627.

$$\left(x^{2}\right)^{627}$$

To raise a power to another power, multiply the exponents.

$$x^{2\times 627}$$

Multiply 2 times 627.

$$x^{1254}$$

Differentiate w.r.t. x

$$1254x^{1253}$$

Steps Using Definition of a Derivative

Calculate 25 to the power of 2 and get 625.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{2}\right)^{2+625})$$

Add 2 and 625 to get 627.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{2}\right)^{627})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 627 to get 1254.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1254})$$

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

$$1254x^{1254-1}$$

Subtract 1 from 1254.

$$1254x^{1253}$$