Solve frac{6x^{5}y^{2}z^3}{3x^2y^3z^2}

$$\frac { 6 x ^ { 5 } y ^ { 2 } z ^ { 3 } } { 3 x ^ { 2 } y ^ { 3 } z ^ { 2 } }$$

Differentiate w.r.t. x

$$\frac{6zx^{2}}{y}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6y^{2}z^{3}}{3z^{2}y^{3}}x^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2z}{y}x^{3})$$

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}.

$$3\times \frac{2z}{y}x^{3-1}$$

Do the arithmetic.

$$\frac{6z}{y}x^{2}$$

Evaluate

$$\frac{2zx^{3}}{y}$$

Solution Steps

Cancel out 3x^{2}y^{2}z^{2} in both numerator and denominator.

$$\frac{2zx^{3}}{y}$$