Solve 5^2x5^3

$${ 5 }^{ 2 } x { 5 }^{ 3 }$$

Evaluate

$$3125x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$5^{5}x$$

Calculate 5 to the power of 5 and get 3125.

$$3125x$$

Differentiate w.r.t. x

$$3125$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

Calculate 5 to the power of 5 and get 3125.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3125x)$$

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

$$3125x^{1-1}$$

Subtract 1 from 1.

$$3125x^{0}$$

For any term t except 0, t^{0}=1.

$$3125\times 1$$

For any term t, t\times 1=t and 1t=t.

$$3125$$