Solve 4y^6*6y^3

$$4 y ^ { 6 } \cdot 6 y ^ { 3 }$$

Evaluate

$$24y^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$4y^{9}\times 6$$

Multiply 4 and 6 to get 24.

$$24y^{9}$$

Differentiate w.r.t. y

$$216y^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y^{9}\times 6)$$

Multiply 4 and 6 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}y}(24y^{9})$$

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

$$9\times 24y^{9-1}$$

Multiply 9 times 24.

$$216y^{9-1}$$

Subtract 1 from 9.

$$216y^{8}$$