Solve 5y^{-2}u^-4*8w^-1w*2y^-4u^4

$$5 y ^ { - 2 } u ^ { - 4 } \cdot 8 w ^ { - 1 } w \cdot 2 y ^ { - 4 } u ^ { 4 }$$

Evaluate

$$\frac{80}{y^{6}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and -4 to get -6.

$$5y^{-6}u^{-4}\times 8w^{-1}w\times 2u^{4}$$

Multiply u^{-4} and u^{4} to get 1.

$$5y^{-6}\times 8w^{-1}w\times 2$$

Multiply w^{-1} and w to get 1.

$$5y^{-6}\times 8\times 2$$

Multiply 5 and 8 to get 40.

$$40y^{-6}\times 2$$

Multiply 40 and 2 to get 80.

$$80y^{-6}$$

Differentiate w.r.t. y

$$-\frac{480}{y^{7}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -2 and -4 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{-6}u^{-4}\times 8w^{-1}w\times 2u^{4})$$

Multiply u^{-4} and u^{4} to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{-6}\times 8w^{-1}w\times 2)$$

Multiply w^{-1} and w to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{-6}\times 8\times 2)$$

Multiply 5 and 8 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}y}(40y^{-6}\times 2)$$

Multiply 40 and 2 to get 80.

$$\frac{\mathrm{d}}{\mathrm{d}y}(80y^{-6})$$

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

$$-6\times 80y^{-6-1}$$

Multiply -6 times 80.

$$-480y^{-6-1}$$

Subtract 1 from -6.

$$-480y^{-7}$$