Solve 60x^4y^2z^3/-12xyz^2=

$$\frac { 60 x ^ { 4 } y ^ { 2 } z ^ { 3 } } { - 12 x y z ^ { 2 } } =$$

Evaluate

$$-5yzx^{3}$$

Solution Steps

Cancel out 12xyz^{2} in both numerator and denominator.

$$\frac{5yzx^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$-5yzx^{3}$$

Differentiate w.r.t. x

$$-15yzx^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{60y^{2}z^{3}}{-12yz^{2}}x^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-5yz\right)x^{3})$$

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}.

$$3\left(-5yz\right)x^{3-1}$$

Do the arithmetic.

$$\left(-15yz\right)x^{2}$$