Solve x^2*(5^2x^2)

$${ x }^{ 2 } \times ( { 5 }^{ 2 } { x }^{ 2 } )$$

Evaluate

$$25x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$x^{4}\times 5^{2}$$

Calculate 5 to the power of 2 and get 25.

$$x^{4}\times 25$$

Differentiate w.r.t. x

$$100x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 5^{2})$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 25)$$

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

$$4\times 25x^{4-1}$$

Multiply 4 times 25.

$$100x^{4-1}$$

Subtract 1 from 4.

$$100x^{3}$$