Solve 8xy*15y/1*4x^2

$$\frac { 8 x y \cdot 15 y } { 1 \cdot 4 x ^ { 2 } }$$

Evaluate

$$\frac{30y^{2}}{x}$$

Solution Steps

Multiply y and y to get y^{2}.

$$\frac{8xy^{2}\times 15}{1\times 4x^{2}}$$

Cancel out 4x in both numerator and denominator.

$$\frac{2\times 15y^{2}}{x}$$

Multiply 2 and 15 to get 30.

$$\frac{30y^{2}}{x}$$

Differentiate w.r.t. x

$$-30\times \left(\frac{y}{x}\right)^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{120y^{2}}{4}x^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30y^{2}\times \frac{1}{x})$$

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}.

$$-30y^{2}x^{-1-1}$$

Do the arithmetic.

$$\left(-30y^{2}\right)x^{-2}$$