Solve (12y*y^3)(y^5)

$$( 12 y \cdot y ^ { 3 } ) ( y ^ { 5 } )$$

Evaluate

$$12y^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$12y^{4}y^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$12y^{9}$$

Differentiate w.r.t. y

$$108y^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(12y^{4}y^{5})$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}y}(12y^{9})$$

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

$$9\times 12y^{9-1}$$

Multiply 9 times 12.

$$108y^{9-1}$$

Subtract 1 from 9.

$$108y^{8}$$