Solve 4y^2*2y^4

$$4 y ^ { 2 } \cdot 2 y ^ { 4 }$$

Evaluate

$$8y^{6}$$

Solution Steps

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

$$4y^{6}\times 2$$

Multiply 4 and 2 to get 8.

$$8y^{6}$$

Differentiate w.r.t. y

$$48y^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(4y^{6}\times 2)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}y}(8y^{6})$$

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

$$6\times 8y^{6-1}$$

Multiply 6 times 8.

$$48y^{6-1}$$

Subtract 1 from 6.

$$48y^{5}$$