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Find the derivative of $-\frac{1}{3}\cos\left(3x\right)$

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Solution

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Final answer to the problem

$\sin\left(3x\right)$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

Simplify the derivative by applying the properties of logarithms

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

$\frac{d}{dx}\left(\frac{-\cos\left(3x\right)}{3}\right)$

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Unlock the first 3 steps of this solution

Learn how to solve differential calculus problems step by step online. Find the derivative of -1/3cos(3x). Simplify the derivative by applying the properties of logarithms. The derivative of a function multiplied by a constant (\frac{1}{3}) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Multiply the fraction and term in -\left(\frac{1}{3}\right)\frac{d}{dx}\left(\cos\left(3x\right)\right).

Final answer to the problem

$\sin\left(3x\right)$

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Function Plot

Plotting: $\sin\left(3x\right)$

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5
6
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

How to improve your answer:

Similar Problems Solved

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$\frac{d}{dx}\left(\sqrt{\sin\left(x\right)}\right)$

$\frac{d}{dx}\left(\sin\left(x\right)\right)^2$

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.

Used Formulas

See formulas (4)

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