Question

Given that y = (x –5)(2x+5)^0.5 ,
find dy/dx

Answer 1

Use product then chain rule:
\[\Large \begin{array}{l}
y = (x - 5){(2x + 5)^{1/2}}\\
u'v + uv'\\
u = (x - 5)\\
u' = 1\\
v = {(2x + 5)^{1/2}}\\
v' = a'[b] \cdot b'\\
a = {b^{1/2}}\\
a' = \frac{1}{2}{b^{ - 1/2}}\\
b = 2x + 5\\
b' = 2\\
v' = \frac{1}{2}{(2x + 5)^{ - 1/2}} \cdot 2 = {(2x + 5)^{ - 1/2}}\\
y' = 1 \cdot {(2x + 5)^{1/2}} + (x - 5) \cdot {(2x + 5)^{ - 1/2}}
\end{array}\]
And simplify.