Solve frac{15x^{6}y^{4}z^3}{20x^3y^4z^6}

$$\frac { 15 x ^ { 6 } y ^ { 4 } z ^ { 3 } } { 20 x ^ { 3 } y ^ { 4 } z ^ { 6 } }$$

Differentiate w.r.t. x

$$\frac{9x^{2}}{4z^{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15z^{3}y^{4}}{20y^{4}z^{6}}x^{6-3})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{4z^{3}}x^{3})$$

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}.

$$3\times \frac{3}{4z^{3}}x^{3-1}$$

Do the arithmetic.

$$\frac{9}{4z^{3}}x^{2}$$

Evaluate

$$\frac{3\times \left(\frac{x}{z}\right)^{3}}{4}$$

Solution Steps

Cancel out 5x^{3}z^{3}y^{4} in both numerator and denominator.

$$\frac{3x^{3}}{4z^{3}}$$