Solve frac{60x^{6}y^{4}z^2}{4x^2y^3z^2}

$$\frac { 60 x ^ { 6 } y ^ { 4 } z ^ { 2 } } { 4 x ^ { 2 } y ^ { 3 } z ^ { 2 } }$$

Differentiate w.r.t. x

$$60yx^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{60z^{2}y^{4}}{4z^{2}y^{3}}x^{6-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15yx^{4})$$

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}.

$$4\times 15yx^{4-1}$$

Do the arithmetic.

$$60yx^{3}$$

Evaluate

$$15yx^{4}$$

Solution Steps

Cancel out 4x^{2}z^{2}y^{3} in both numerator and denominator.

$$15yx^{4}$$