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Find the derivative of $y\left(2+\sin\left(x\right)\right)$

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Solution

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Final answer to the problem

$y\cos\left(x\right)$
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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 function multiplied by a constant is equal to the constant times the derivative of the function

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

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

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

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Learn how to solve differential calculus problems step by step online. Find the derivative of y(2+sin(x)). The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}.

Final answer to the problem

$y\cos\left(x\right)$

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Function Plot

Plotting: $y\cos\left(x\right)$

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5
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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

How to improve your answer:

Similar Problems Solved

Find the derivative

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

$\frac{d}{dx}\left(\arctan\left(x-\sqrt{1+x^2}\right)\right)$

$\frac{d}{dx}\arctan\left(x-\sqrt{1+x^2}\right)$

$\frac{d}{dx}\arccos\left(\sqrt{1-x^2}\right)$

$\frac{d}{dx}\left(\mathrm{sech}\left(-4x\right)\left(1-\ln\left(\mathrm{sech}\left(-4x\right)\right)\right)\right)$

$\frac{d}{dx}\left(\ln\left(\mathrm{sech}\left(3x+8\right)\right)\right)$

$\frac{d}{dx}\ln\left(x^2+1\right)$

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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