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Find the implicit derivative $\frac{d}{dx}\left(\sin\left(x+5y\right)\right)=6x$

Step-by-step Solution

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Final Answer

$y^{\prime}=\frac{6x-\cos\left(x+5y\right)}{5\cos\left(x+5y\right)}$
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Step-by-step Solution

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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 ${f'(x) = \cos(x)\cdot D_x(x)}$

$\frac{d}{dx}\left(x+5y\right)\cos\left(x+5y\right)=6x$

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$\frac{d}{dx}\left(x+5y\right)\cos\left(x+5y\right)=6x$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(sin(x+5y))=6x. 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)}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function is equal to 1. The derivative of the linear function times a constant, is equal to the constant.

Final Answer

$y^{\prime}=\frac{6x-\cos\left(x+5y\right)}{5\cos\left(x+5y\right)}$

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Function Plot

Plotting: $y^{\prime}=\frac{6x-\cos\left(x+5y\right)}{5\cos\left(x+5y\right)}$

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1
2
3
4
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
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

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