Solve (3s^5)(-4s^-6)

$$( 3 s ^ { 5 } ) ( - 4 s ^ { - 6 } )$$

Evaluate

$$-\frac{12}{s}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and -6 to get -1.

$$3s^{-1}\left(-4\right)$$

Multiply 3 and -4 to get -12.

$$-12s^{-1}$$

Differentiate w.r.t. s

$$\frac{12}{s^{2}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and -6 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}s}(3s^{-1}\left(-4\right))$$

Multiply 3 and -4 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}s}(-12s^{-1})$$

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

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

Multiply -1 times -12.

$$12s^{-1-1}$$

Subtract 1 from -1.

$$12s^{-2}$$