Solve 12x^3y/5zdiv4x^2y^2/15yz=

$$\frac { 12 x ^ { 3 } y } { 5 z } \div \frac { 4 x ^ { 2 } y ^ { 2 } } { 15 y z } =$$

Evaluate

$$9x$$

Solution Steps

Divide \frac{12x^{3}y}{5z} by \frac{4x^{2}y^{2}}{15yz} by multiplying \frac{12x^{3}y}{5z} by the reciprocal of \frac{4x^{2}y^{2}}{15yz}.

$$\frac{12x^{3}y\times 15yz}{5z\times 4x^{2}y^{2}}$$

Cancel out 4\times 5yyzx^{2} in both numerator and denominator.

$$3\times 3x$$

Multiply 3 and 3 to get 9.

$$9x$$

Differentiate w.r.t. x

$$9$$

Steps Using Definition of a Derivative

Divide \frac{12x^{3}y}{5z} by \frac{4x^{2}y^{2}}{15yz} by multiplying \frac{12x^{3}y}{5z} by the reciprocal of \frac{4x^{2}y^{2}}{15yz}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12x^{3}y\times 15yz}{5z\times 4x^{2}y^{2}})$$

Cancel out 4\times 5yyzx^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3\times 3x)$$

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x)$$

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

$$9x^{1-1}$$

Subtract 1 from 1.

$$9x^{0}$$

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

$$9\times 1$$

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

$$9$$