Solve 7x/1*13x/14y*(-12y^2/13x^2)=

$$\frac { 7 x } { 1 } \cdot \frac { 13 x } { 14 y } \cdot ( - \frac { 12 y ^ { 2 } } { 13 x ^ { 2 } } ) =$$

Evaluate

$$-6y$$

Solution Steps

Anything divided by one gives itself.

$$7x\times \frac{13x}{14y}\left(-\frac{12y^{2}}{13x^{2}}\right)$$

Express 7\times \frac{13x}{14y} as a single fraction.

$$\frac{7\times 13x}{14y}x\left(-\frac{12y^{2}}{13x^{2}}\right)$$

Cancel out 7 in both numerator and denominator.

$$\frac{13x}{2y}x\left(-\frac{12y^{2}}{13x^{2}}\right)$$

Multiply \frac{13x}{2y} times -\frac{12y^{2}}{13x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-13x\times 12y^{2}}{2y\times 13x^{2}}x$$

Cancel out 2\times 13xy in both numerator and denominator.

$$\frac{-6y}{x}x$$

Cancel out x and x.

$$-6y$$

Differentiate w.r.t. y

$$-6$$

Steps Using Definition of a Derivative

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}y}(7x\times \frac{13x}{14y}\left(-\frac{12y^{2}}{13x^{2}}\right))$$

Express 7\times \frac{13x}{14y} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{7\times 13x}{14y}x\left(-\frac{12y^{2}}{13x^{2}}\right))$$

Cancel out 7 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{13x}{2y}x\left(-\frac{12y^{2}}{13x^{2}}\right))$$

Multiply \frac{13x}{2y} times -\frac{12y^{2}}{13x^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{-13x\times 12y^{2}}{2y\times 13x^{2}}x)$$

Cancel out 2\times 13xy in both numerator and denominator.

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

Cancel out x and x.

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

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.

$$-6$$