Solve (4y^5)(3y^5)

$$( 4 y ^ { 5 } ) ( 3 y ^ { 5 } )$$

Evaluate

$$12y^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$4y^{10}\times 3$$

Multiply 4 and 3 to get 12.

$$12y^{10}$$

Differentiate w.r.t. y

$$120y^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y^{10}\times 3)$$

Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}y}(12y^{10})$$

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

$$10\times 12y^{10-1}$$

Multiply 10 times 12.

$$120y^{10-1}$$

Subtract 1 from 10.

$$120y^{9}$$