Solve {left(-1/3right)}^2x{left(-1/3right)}^3

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

Evaluate

$$-\frac{x}{243}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\left(-\frac{1}{3}\right)^{5}x$$

Calculate -\frac{1}{3} to the power of 5 and get -\frac{1}{243}.

$$-\frac{1}{243}x$$

Differentiate w.r.t. x

$$-\frac{1}{243} = -0.00411522633744856$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{1}{3}\right)^{5}x)$$

Calculate -\frac{1}{3} to the power of 5 and get -\frac{1}{243}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{1}{243}x)$$

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

$$-\frac{1}{243}x^{1-1}$$

Subtract 1 from 1.

$$-\frac{1}{243}x^{0}$$

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

$$-\frac{1}{243}$$