Solve 4x^2y^3/xy=

$$\frac { 4 x ^ { 2 } y ^ { 3 } } { x y } =$$

Differentiate w.r.t. x

$$4y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4y^{3}}{y}x^{2-1})$$

Do the arithmetic.

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

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}.

$$4y^{2}x^{1-1}$$

Do the arithmetic.

$$4y^{2}x^{0}$$

For any term t except 0, t^{0}=1.

$$4y^{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$4y^{2}$$

Evaluate

$$4xy^{2}$$

Solution Steps

Cancel out xy in both numerator and denominator.

$$4xy^{2}$$