Solve xsqrt{5*5^}

$$x \sqrt{ 5 \times { 5 }^{ } }$$

Evaluate

$$5x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

$$x\sqrt{5^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$x\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$x\times 5$$

Differentiate w.r.t. x

$$5$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

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

Calculate 5 to the power of 2 and get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{25})$$

Calculate the square root of 25 and get 5.

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

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

$$5x^{1-1}$$

Subtract 1 from 1.

$$5x^{0}$$

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

$$5\times 1$$

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

$$5$$