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Differentiate w.r.t. x
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\frac{7\times 5}{45x}+\frac{8\times 9}{45x}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9x and 5x is 45x. Multiply \frac{7}{9x} times \frac{5}{5}. Multiply \frac{8}{5x} times \frac{9}{9}.
\frac{7\times 5+8\times 9}{45x}
Since \frac{7\times 5}{45x} and \frac{8\times 9}{45x} have the same denominator, add them by adding their numerators.
\frac{35+72}{45x}
Do the multiplications in 7\times 5+8\times 9.
\frac{107}{45x}
Do the calculations in 35+72.