Solve 9/4x^2/frac{6x{16x^4}}

$$\frac { \frac { 9 } { 4 x ^ { 2 } } } { \frac { 6 x } { 16 x ^ { 4 } } }$$

Evaluate

$$6x$$

Solution Steps

Divide \frac{9}{4x^{2}} by \frac{6x}{16x^{4}} by multiplying \frac{9}{4x^{2}} by the reciprocal of \frac{6x}{16x^{4}}.

$$\frac{9\times 16x^{4}}{4x^{2}\times 6x}$$

Cancel out 2\times 3\times 4xx^{2} in both numerator and denominator.

$$2\times 3x$$

Multiply 2 and 3 to get 6.

$$6x$$

Differentiate w.r.t. x

$$6$$

Steps Using Definition of a Derivative

Divide \frac{9}{4x^{2}} by \frac{6x}{16x^{4}} by multiplying \frac{9}{4x^{2}} by the reciprocal of \frac{6x}{16x^{4}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9\times 16x^{4}}{4x^{2}\times 6x})$$

Cancel out 2\times 3\times 4xx^{2} in both numerator and denominator.

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

Multiply 2 and 3 to get 6.

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

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

$$6x^{1-1}$$

Subtract 1 from 1.

$$6x^{0}$$

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

$$6\times 1$$

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

$$6$$