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Find the derivative of $\sqrt{3}z+4=-\sqrt{3}z+8$ using the definition

Step-by-step Solution

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Solution

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Final answer to the problem

$-\sqrt{3}$
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Step-by-step Solution

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Calculate the square root of $3$

$derivdef\left(-\sqrt{3}z+8\right)$

Learn how to solve sum rule of differentiation problems step by step online.

$derivdef\left(-\sqrt{3}z+8\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of z3^1/2+4=-3^1/2z+8 using the definition. Calculate the square root of 3. Multiply -1 times \sqrt{3}. Find the derivative of -\sqrt{3}z+8 using the definition. Apply the definition of the derivative: \displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}. The function f(x) is the function we want to differentiate, which is -\sqrt{3}z+8. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -\sqrt{3} by each term of the polynomial \left(z+h\right).

Final answer to the problem

$-\sqrt{3}$

Explore different ways to solve this problem

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 derivdef(-13^0.5+8) using the product ruleFind derivdef(-13^0.5+8) using the quotient ruleFind derivdef(-13^0.5+8) using logarithmic differentiation

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Function Plot

Plotting: $-\sqrt{3}$

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7
8
9
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: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

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