Solve 3y^2*4y^3

$$3 y ^ { 2 } \times 4 y ^ { 3 }$$

Evaluate

$$12y^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$3y^{5}\times 4$$

Multiply 3 and 4 to get 12.

$$12y^{5}$$

Differentiate w.r.t. y

$$60y^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{5}\times 4)$$

Multiply 3 and 4 to get 12.

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

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

$$5\times 12y^{5-1}$$

Multiply 5 times 12.

$$60y^{5-1}$$

Subtract 1 from 5.

$$60y^{4}$$