Solve 7(x^3)^-2

$$7 ( x ^ { 3 } ) ^ { - 2 }$$

Differentiate w.r.t. x

$$-\frac{42}{x^{7}}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{-6})$$

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

$$-6\times 7x^{-6-1}$$

Multiply -6 times 7.

$$-42x^{-6-1}$$

Subtract 1 from -6.

$$-42x^{-7}$$

Evaluate

$$\frac{7}{x^{6}}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$7x^{-6}$$