Solve 5sqrt{2a}*3/10sqrt{2a}

$$5 \sqrt { 2 a } \times \frac { 3 } { 10 } \sqrt { 2 a }$$

Evaluate

$$3a$$

Solution Steps

Multiply \sqrt{2a} and \sqrt{2a} to get \left(\sqrt{2a}\right)^{2}.

$$5\left(\sqrt{2a}\right)^{2}\times \frac{3}{10}$$

Calculate \sqrt{2a} to the power of 2 and get 2a.

$$5\times 2a\times \frac{3}{10}$$

Multiply 5 and 2 to get 10.

$$10a\times \frac{3}{10}$$

Cancel out 10 and 10.

$$3a$$

Differentiate w.r.t. a

$$3$$

Steps Using Definition of a Derivative

Multiply \sqrt{2a} and \sqrt{2a} to get \left(\sqrt{2a}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5\left(\sqrt{2a}\right)^{2}\times \frac{3}{10})$$

Calculate \sqrt{2a} to the power of 2 and get 2a.

$$\frac{\mathrm{d}}{\mathrm{d}a}(5\times 2a\times \frac{3}{10})$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(10a\times \frac{3}{10})$$

Cancel out 10 and 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3a)$$

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

$$3a^{1-1}$$

Subtract 1 from 1.

$$3a^{0}$$

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

$$3\times 1$$

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

$$3$$