Solve 5y^3*2y^2

$$5 y ^ { 3 } \times 2 y ^ { 2 }$$

Evaluate

$$10y^{5}$$

Solution Steps

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

$$5y^{5}\times 2$$

Multiply 5 and 2 to get 10.

$$10y^{5}$$

Differentiate w.r.t. y

$$50y^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{5}\times 2)$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}y}(10y^{5})$$

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

$$5\times 10y^{5-1}$$

Multiply 5 times 10.

$$50y^{5-1}$$

Subtract 1 from 5.

$$50y^{4}$$