Solve (2xy^2z/wt^2)*(3wt^2/xyz)=

$$( 2 \frac { x y ^ { 2 } z } { w t ^ { 2 } } ) \cdot ( \frac { 3 w t ^ { 2 } } { x y z } ) =$$

Evaluate

$$6y$$

Solution Steps

Express 2\times \frac{xy^{2}z}{wt^{2}} as a single fraction.

$$\frac{2xy^{2}z}{wt^{2}}\times \frac{3wt^{2}}{xyz}$$

Multiply \frac{2xy^{2}z}{wt^{2}} times \frac{3wt^{2}}{xyz} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2xy^{2}z\times 3wt^{2}}{wt^{2}xyz}$$

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

$$2\times 3y$$

Multiply 2 and 3 to get 6.

$$6y$$

Differentiate w.r.t. y

$$6$$

Steps Using Definition of a Derivative

Express 2\times \frac{xy^{2}z}{wt^{2}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2xy^{2}z}{wt^{2}}\times \frac{3wt^{2}}{xyz})$$

Multiply \frac{2xy^{2}z}{wt^{2}} times \frac{3wt^{2}}{xyz} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{2xy^{2}z\times 3wt^{2}}{wt^{2}xyz})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(2\times 3y)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(6y)$$

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

$$6y^{1-1}$$

Subtract 1 from 1.

$$6y^{0}$$

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

$$6\times 1$$

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

$$6$$