Solve a|sqrt[6]{9^6}

$$a | \sqrt[ 6 ] { 9 ^ { 6 } }$$

Evaluate

$$9a$$

Solution Steps

Calculate 9 to the power of 6 and get 531441.

$$a|\sqrt[6]{531441}|$$

Calculate \sqrt[6]{531441} and get 9.

$$a|9|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 9 is 9.

$$a\times 9$$

Differentiate w.r.t. a

$$9$$

Steps Using Definition of a Derivative

Calculate 9 to the power of 6 and get 531441.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|\sqrt[6]{531441}|)$$

Calculate \sqrt[6]{531441} and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a|9|)$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 9 is 9.

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

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

$$9a^{1-1}$$

Subtract 1 from 1.

$$9a^{0}$$

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

$$9\times 1$$

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

$$9$$