Solve 5x^7y^3/x^2y=

$$\frac { 5 x ^ { 7 } y ^ { 3 } } { x ^ { 2 } y } =$$

Differentiate w.r.t. x

$$25y^{2}x^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{3}}{y}x^{7-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5y^{2}x^{5})$$

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}.

$$5\times 5y^{2}x^{5-1}$$

Do the arithmetic.

$$25y^{2}x^{4}$$

Evaluate

$$5y^{2}x^{5}$$

Solution Steps

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

$$5y^{2}x^{5}$$