Solve 5y^5quad5y^5

$$5 y ^ { 5 } \quad 5 y ^ { 5 }$$

Evaluate

$$25y^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

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

Multiply 5 and 5 to get 25.

$$25y^{10}$$

Differentiate w.r.t. y

$$250y^{9}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 5 to get 10.

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

Multiply 5 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}y}(25y^{10})$$

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

$$10\times 25y^{10-1}$$

Multiply 10 times 25.

$$250y^{10-1}$$

Subtract 1 from 10.

$$250y^{9}$$