Find the derivative $\frac{d}{dx}\left(\sin\left(x\right)-\tan\left(x\right)\cos\left(x\right)\right)$ using the sum rule

Step-by-step Solution

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Final answer to the problem

$\cos\left(x\right)-\sec\left(x\right)+\tan\left(x\right)\sin\left(x\right)$
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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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The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(-\tan\left(x\right)\cos\left(x\right)\right)$

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

$\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(-\tan\left(x\right)\cos\left(x\right)\right)$

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Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(sin(x)-tan(x)cos(x)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\tan\left(x\right) and g=\cos\left(x\right). Simplify the product -(\frac{d}{dx}\left(\tan\left(x\right)\right)\cos\left(x\right)+\tan\left(x\right)\frac{d}{dx}\left(\cos\left(x\right)\right)).

Final answer to the problem

$\cos\left(x\right)-\sec\left(x\right)+\tan\left(x\right)\sin\left(x\right)$

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Function Plot

Plotting: $\cos\left(x\right)-\sec\left(x\right)+\tan\left(x\right)\sin\left(x\right)$

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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
Dx
|◻|
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:

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.

Used Formulas

See formulas (7)

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