Solve frac{6x^{3}y^{4}z^2}{3x^2y^2z^2}

$$\frac { 6 x ^ { 3 } y ^ { 4 } z ^ { 2 } } { 3 x ^ { 2 } y ^ { 2 } z ^ { 2 } }$$

Differentiate w.r.t. x

$$2y^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6z^{2}y^{4}}{3y^{2}z^{2}}x^{3-2})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

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

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

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

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

$$2y^{2}$$

Evaluate

$$2xy^{2}$$

Solution Steps

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

$$2xy^{2}$$