Solve -6x^-5*30^-1

$$- 6 x ^ { - 5 } \cdot 30 ^ { - 1 }$$

Evaluate

$$-\frac{1}{5x^{5}}$$

Solution Steps

Calculate 30 to the power of -1 and get \frac{1}{30}.

$$-6x^{-5}\times \frac{1}{30}$$

Multiply -6 and \frac{1}{30} to get -\frac{1}{5}.

$$-\frac{1}{5}x^{-5}$$

Differentiate w.r.t. x

$$\frac{1}{x^{6}}$$

Steps Using Definition of a Derivative

Calculate 30 to the power of -1 and get \frac{1}{30}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{-5}\times \frac{1}{30})$$

Multiply -6 and \frac{1}{30} to get -\frac{1}{5}.

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

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

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

Multiply -5 times -\frac{1}{5}.

$$x^{-5-1}$$

Subtract 1 from -5.

$$x^{-6}$$