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Find the derivative of $\frac{\left(\sqrt{a+5}-3\right)\left(\sqrt{a}+2\right)}{a-4}$

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Solution

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Final Answer

$\frac{2\left(\sqrt{a}\sqrt{a+5}-2\sqrt{a+5}\right)\sqrt{a}-2\sqrt{\left(a+5\right)^{3}}+6\left(a+5\right)}{4\left(a+5\right)\sqrt{a}\left(\sqrt{a}-2\right)^2}$
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Step-by-step Solution

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Simplify $\frac{\left(\sqrt{a+5}-3\right)\left(\sqrt{a}+2\right)}{a-4}$

$\frac{d}{da}\left(\frac{\sqrt{a+5}-3}{\sqrt{a}-1\cdot 2}\right)$

Learn how to solve differential calculus problems step by step online.

$\frac{d}{da}\left(\frac{\sqrt{a+5}-3}{\sqrt{a}-1\cdot 2}\right)$

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Learn how to solve differential calculus problems step by step online. Find the derivative of (((a+5)^1/2-3)(a^1/2+2))/(a-4). Simplify \frac{\left(\sqrt{a+5}-3\right)\left(\sqrt{a}+2\right)}{a-4}. Multiply -1 times 2. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Simplify the product -(\sqrt{a+5}-3).

Final Answer

$\frac{2\left(\sqrt{a}\sqrt{a+5}-2\sqrt{a+5}\right)\sqrt{a}-2\sqrt{\left(a+5\right)^{3}}+6\left(a+5\right)}{4\left(a+5\right)\sqrt{a}\left(\sqrt{a}-2\right)^2}$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Find the derivativeFind derivative of ((a+5)^0.5-3)(a^0.5+2)/(a-4) using the product ruleFind derivative of ((a+5)^0.5-3)(a^0.5+2)/(a-4) using the quotient ruleFind derivative of ((a+5)^0.5-3)(a^0.5+2)/(a-4) using logarithmic differentiationFind derivative of ((a+5)^0.5-3)(a^0.5+2)/(a-4) using the definition

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Function Plot

Plotting: $\frac{2\left(\sqrt{a}\sqrt{a+5}-2\sqrt{a+5}\right)\sqrt{a}-2\sqrt{\left(a+5\right)^{3}}+6\left(a+5\right)}{4\left(a+5\right)\sqrt{a}\left(\sqrt{a}-2\right)^2}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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