Solve 75y^3175y^2

$$75 y ^ { 3 } 175 y ^ { 2 }$$

Evaluate

$$13125y^{5}$$

Solution Steps

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

$$75y^{5}\times 175$$

Multiply 75 and 175 to get 13125.

$$13125y^{5}$$

Differentiate w.r.t. y

$$65625y^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(75y^{5}\times 175)$$

Multiply 75 and 175 to get 13125.

$$\frac{\mathrm{d}}{\mathrm{d}y}(13125y^{5})$$

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

$$5\times 13125y^{5-1}$$

Multiply 5 times 13125.

$$65625y^{5-1}$$

Subtract 1 from 5.

$$65625y^{4}$$