Solve 4sqrt{a}*4sqrt{a}

$$4 \sqrt { a } \cdot 4 \sqrt { a }$$

Evaluate

$$16a$$

Solution Steps

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

$$4\times 4\left(\sqrt{a}\right)^{2}$$

Multiply 4 and 4 to get 16.

$$16\left(\sqrt{a}\right)^{2}$$

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

$$16a$$

Differentiate w.r.t. a

$$16$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(4\times 4\left(\sqrt{a}\right)^{2})$$

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(16\left(\sqrt{a}\right)^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(16a)$$

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

$$16a^{1-1}$$

Subtract 1 from 1.

$$16a^{0}$$

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

$$16\times 1$$

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

$$16$$