Solve (3sqrt{6}sqrt{a}9)4*(3sqrt{6}sqrt{a}9)4

$$( 3 \sqrt { 6 } \sqrt { a } 9 ) 4 \cdot ( 3 \sqrt { 6 } \sqrt { a } 9 ) 4$$

Evaluate

$$69984a$$

Solution Steps

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$4\times 4\times 3\times 9\times 6\sqrt{a}\times 3\times 9\sqrt{a}$$

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

$$4\times 4\times 3\times 9\times 6\left(\sqrt{a}\right)^{2}\times 3\times 9$$

Multiply 4 and 4 to get 16.

$$16\times 3\times 9\times 6\left(\sqrt{a}\right)^{2}\times 3\times 9$$

Multiply 16 and 3 to get 48.

$$48\times 9\times 6\left(\sqrt{a}\right)^{2}\times 3\times 9$$

Multiply 48 and 9 to get 432.

$$432\times 6\left(\sqrt{a}\right)^{2}\times 3\times 9$$

Multiply 432 and 6 to get 2592.

$$2592\left(\sqrt{a}\right)^{2}\times 3\times 9$$

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

$$2592a\times 3\times 9$$

Multiply 2592 and 3 to get 7776.

$$7776a\times 9$$

Multiply 7776 and 9 to get 69984.

$$69984a$$

Differentiate w.r.t. a

$$69984$$

Steps Using Definition of a Derivative

Multiply \sqrt{6} and \sqrt{6} to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4\times 4\times 3\times 9\times 6\sqrt{a}\times 3\times 9\sqrt{a})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(4\times 4\times 3\times 9\times 6\left(\sqrt{a}\right)^{2}\times 3\times 9)$$

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(16\times 3\times 9\times 6\left(\sqrt{a}\right)^{2}\times 3\times 9)$$

Multiply 16 and 3 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}a}(48\times 9\times 6\left(\sqrt{a}\right)^{2}\times 3\times 9)$$

Multiply 48 and 9 to get 432.

$$\frac{\mathrm{d}}{\mathrm{d}a}(432\times 6\left(\sqrt{a}\right)^{2}\times 3\times 9)$$

Multiply 432 and 6 to get 2592.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2592\left(\sqrt{a}\right)^{2}\times 3\times 9)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(2592a\times 3\times 9)$$

Multiply 2592 and 3 to get 7776.

$$\frac{\mathrm{d}}{\mathrm{d}a}(7776a\times 9)$$

Multiply 7776 and 9 to get 69984.

$$\frac{\mathrm{d}}{\mathrm{d}a}(69984a)$$

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

$$69984a^{1-1}$$

Subtract 1 from 1.

$$69984a^{0}$$

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

$$69984\times 1$$

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

$$69984$$