Solve dx/d(frac{1{3})^2}

$$\frac { d x } { d ( \frac { 1 } { 3 } ) ^ { 2 } }$$

Evaluate

$$9x$$

Solution Steps

Cancel out d in both numerator and denominator.

$$\frac{x}{\left(\frac{1}{3}\right)^{2}}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{x}{\frac{1}{9}}$$

Divide x by \frac{1}{9} by multiplying x by the reciprocal of \frac{1}{9}.

$$x\times 9$$

Differentiate w.r.t. x

$$9$$

Steps Using Definition of a Derivative

Cancel out d in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(\frac{1}{3}\right)^{2}})$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\frac{1}{9}})$$

Divide x by \frac{1}{9} by multiplying x by the reciprocal of \frac{1}{9}.

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

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

$$9x^{1-1}$$

Subtract 1 from 1.

$$9x^{0}$$

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

$$9\times 1$$

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

$$9$$