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Find the derivative of $-\frac{2}{3}p+\frac{1}{5}-1+\frac{5}{6}p$ using the definition

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{1}{6}$
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Step-by-step Solution

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Subtract the values $\frac{1}{5}$ and $-1$

$derivdef\left(-\frac{4}{5}-\frac{2}{3}p+\frac{5}{6}p\right)$

Learn how to solve definition of derivative problems step by step online.

$derivdef\left(-\frac{4}{5}-\frac{2}{3}p+\frac{5}{6}p\right)$

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Learn how to solve definition of derivative problems step by step online. Find the derivative of -2/3p+1/5+-15/6p using the definition. Subtract the values \frac{1}{5} and -1. Combining like terms -\frac{2}{3}p and \frac{5}{6}p. Find the derivative of -\frac{4}{5}+\frac{1}{6}p 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 -\frac{4}{5}+\frac{1}{6}p. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term \frac{1}{6} by each term of the polynomial \left(p+h\right).

Final answer to the problem

$\frac{1}{6}$

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(-0.6667p+0.2) using the product ruleFind derivdef(-0.6667p+0.2) using the quotient ruleFind derivdef(-0.6667p+0.2) using logarithmic differentiation

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Function Plot

Plotting: $\frac{1}{6}$

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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: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

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See formulas (1)

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