Solve (4y^-12)(10y^6)=

$$( 4 y ^ { - 12 } ) ( 10 y ^ { 6 } ) =$$

Evaluate

$$\frac{40}{y^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -12 and 6 to get -6.

$$4y^{-6}\times 10$$

Multiply 4 and 10 to get 40.

$$40y^{-6}$$

Differentiate w.r.t. y

$$-\frac{240}{y^{7}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -12 and 6 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y^{-6}\times 10)$$

Multiply 4 and 10 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}y}(40y^{-6})$$

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

$$-6\times 40y^{-6-1}$$

Multiply -6 times 40.

$$-240y^{-6-1}$$

Subtract 1 from -6.

$$-240y^{-7}$$