Solve 3n*5n^2/4n^2

$$\frac { 3 n \cdot 5 n ^ { 2 } } { 4 n ^ { 2 } }$$

Evaluate

$$\frac{15n}{4}$$

Solution Steps

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

$$\frac{3n^{3}\times 5}{4n^{2}}$$

Cancel out n^{2} in both numerator and denominator.

$$\frac{3\times 5n}{4}$$

Multiply 3 and 5 to get 15.

$$\frac{15n}{4}$$

Differentiate w.r.t. n

$$\frac{15}{4} = 3\frac{3}{4} = 3.75$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{15n^{2}}{4}n^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{15n^{2}}{4}\times \frac{1}{n})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-\frac{15n^{2}}{4}n^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{15n^{2}}{4}\right)n^{-2}$$