Solve 15n^2div25n

$$15 n ^ { 2 } \div 25 n$$

Evaluate

$$\frac{3n^{3}}{5}$$

Solution Steps

Divide 15n^{2} by 25 to get \frac{3}{5}n^{2}.

$$\frac{3}{5}n^{2}n$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{3}{5}n^{3}$$

Differentiate w.r.t. n

$$\frac{9n^{2}}{5}$$

Steps Using Definition of a Derivative

Divide 15n^{2} by 25 to get \frac{3}{5}n^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3}{5}n^{2}n)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3}{5}n^{3})$$

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

$$3\times \frac{3}{5}n^{3-1}$$

Multiply 3 times \frac{3}{5}.

$$\frac{9}{5}n^{3-1}$$

Subtract 1 from 3.

$$\frac{9}{5}n^{2}$$