Solve frac{18x^{6}y^2z^5}{6x^3yz^2}

$$\frac { 18 x ^ { 6 } y ^ { 2 } z ^ { 5 } } { 6 x ^ { 3 } y z ^ { 2 } }$$

Differentiate w.r.t. x

$$9yx^{2}z^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18y^{2}z^{5}}{6yz^{2}}x^{6-3})$$

Do the arithmetic.

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

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}.

$$3\times 3yz^{3}x^{3-1}$$

Do the arithmetic.

$$9yz^{3}x^{2}$$

Evaluate

$$3y\left(xz\right)^{3}$$

Solution Steps

Cancel out 6yz^{2}x^{3} in both numerator and denominator.

$$3yx^{3}z^{3}$$