Solve 77*1*7/9*8*6/7x

$$77 \cdot 1 \cdot \frac { 7 } { 9 \cdot 8 } \cdot \frac { 6 } { 7 } x$$

Evaluate

$$\frac{77x}{12}$$

Solution Steps

Multiply 77 and 1 to get 77.

$$77\times \frac{7}{9\times 8}\times \frac{6}{7}x$$

Multiply 9 and 8 to get 72.

$$77\times \frac{7}{72}\times \frac{6}{7}x$$

Express 77\times \frac{7}{72} as a single fraction.

$$\frac{77\times 7}{72}\times \frac{6}{7}x$$

Multiply 77 and 7 to get 539.

$$\frac{539}{72}\times \frac{6}{7}x$$

Multiply \frac{539}{72} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{539\times 6}{72\times 7}x$$

Do the multiplications in the fraction \frac{539\times 6}{72\times 7}.

$$\frac{3234}{504}x$$

Reduce the fraction \frac{3234}{504} to lowest terms by extracting and canceling out 42.

$$\frac{77}{12}x$$

Differentiate w.r.t. x

$$\frac{77}{12} = 6\frac{5}{12} = 6.416666666666667$$

Steps Using Definition of a Derivative

Multiply 77 and 1 to get 77.

$$\frac{\mathrm{d}}{\mathrm{d}x}(77\times \frac{7}{9\times 8}\times \frac{6}{7}x)$$

Multiply 9 and 8 to get 72.

$$\frac{\mathrm{d}}{\mathrm{d}x}(77\times \frac{7}{72}\times \frac{6}{7}x)$$

Express 77\times \frac{7}{72} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{77\times 7}{72}\times \frac{6}{7}x)$$

Multiply 77 and 7 to get 539.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{539}{72}\times \frac{6}{7}x)$$

Multiply \frac{539}{72} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{539\times 6}{72\times 7}x)$$

Do the multiplications in the fraction \frac{539\times 6}{72\times 7}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3234}{504}x)$$

Reduce the fraction \frac{3234}{504} to lowest terms by extracting and canceling out 42.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{77}{12}x)$$

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

$$\frac{77}{12}x^{1-1}$$

Subtract 1 from 1.

$$\frac{77}{12}x^{0}$$

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

$$\frac{77}{12}\times 1$$

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

$$\frac{77}{12}$$