Solve 6x^{6}y^{6}z^{5}div(-3x^2y^4z)div(-2x^4yz^4)

$$6 x ^ { 6 } y ^ { 6 } z ^ { 5 } \div ( - 3 x ^ { 2 } y ^ { 4 } z ) \div ( - 2 x ^ { 4 } y z ^ { 4 } )$$

Evaluate

$$y$$

Solution Steps

Express \frac{\frac{6x^{6}y^{6}z^{5}}{-3x^{2}y^{4}z}}{-2x^{4}yz^{4}} as a single fraction.

$$\frac{6x^{6}y^{6}z^{5}}{-3x^{2}y^{4}z\left(-2\right)x^{4}yz^{4}}$$

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

$$\frac{y}{-\left(-1\right)}$$

Multiply -1 and -1 to get 1.

$$\frac{y}{1}$$

Anything divided by one gives itself.

$$y$$

Differentiate w.r.t. y

$$1$$

Steps Using Definition of a Derivative

Express \frac{\frac{6x^{6}y^{6}z^{5}}{-3x^{2}y^{4}z}}{-2x^{4}yz^{4}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{6x^{6}y^{6}z^{5}}{-3x^{2}y^{4}z\left(-2\right)x^{4}yz^{4}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{-\left(-1\right)})$$

Multiply -1 and -1 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y)$$

The derivative of ax^{n} is nax^{n-1}.

$$y^{1-1}$$

Subtract 1 from 1.

$$y^{0}$$

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

$$1$$