Solve (3y^-3)(-4y^-3)

$$( 3 y ^ { - 3 } ) ( - 4 y ^ { - 3 } )$$

Evaluate

$$-\frac{12}{y^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -3 and -3 to get -6.

$$3y^{-6}\left(-4\right)$$

Multiply 3 and -4 to get -12.

$$-12y^{-6}$$

Differentiate w.r.t. y

$$\frac{72}{y^{7}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -3 and -3 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{-6}\left(-4\right))$$

Multiply 3 and -4 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-12y^{-6})$$

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

$$-6\left(-12\right)y^{-6-1}$$

Multiply -6 times -12.

$$72y^{-6-1}$$

Subtract 1 from -6.

$$72y^{-7}$$