Solve (5y^-2)(2y)(y^5)

$$( 5 y ^ { - 2 } ) ( 2 y ) ( y ^ { 5 } )$$

Evaluate

$$10y^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 1 to get -1.

$$5y^{-1}\times 2y^{5}$$

To multiply powers of the same base, add their exponents. Add -1 and 5 to get 4.

$$5y^{4}\times 2$$

Multiply 5 and 2 to get 10.

$$10y^{4}$$

Differentiate w.r.t. y

$$40y^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -2 and 1 to get -1.

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

To multiply powers of the same base, add their exponents. Add -1 and 5 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{4}\times 2)$$

Multiply 5 and 2 to get 10.

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

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

$$4\times 10y^{4-1}$$

Multiply 4 times 10.

$$40y^{4-1}$$

Subtract 1 from 4.

$$40y^{3}$$