Thed denominater of a rational number 9 is
Answers
Answer:
hi friend
Step-by-step explanation:
your answer is 1
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Answer:
\begin{gathered} \red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: \: TO \: \: FIND \: \: \: \maltese }}}}} \\ \\ \huge \mathfrak{Derivative \: \: of } \\ \\ \bf \frac{x+cosx}{tanx} \end{gathered}
✠ TOFIND ✠
✠ TOFIND ✠
Derivativeof
tanx
x+cosx
\orange{\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: \: REQUIRED \: \: INFO \: \: \: \maltese }}}}}
✠ REQUIREDINFO ✠
✠ REQUIREDINFO ✠
\begin{gathered} \bigstar \: \: \: \mathfrak{ \underline{\huge Quotient \: \: Rule}} \\ \\ \bf \frac{d}{dx} \frac{u}{v} = \frac{v . \frac{du}{dx} - u \frac{dv}{dx} }{v {}^{2} } \\ \\ \bigstar \bf \: \: \: \frac{d}{dx} cosx = - sinx \\ \\ \bigstar \: \: \: \bf \frac{d}{dx} tanx = {sec}^{2} x\end{gathered}
★
QuotientRule
dx
d
v
u
=
v
2
v.
dx
du
−u
dx
dv
★
dx
d
cosx=−sinx
★
dx
d
tanx=sec
2
x
\green{ \large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: \: SOLUTION \: \: \: \maltese }}}}}
✠ SOLUTION ✠
✠ SOLUTION ✠
\begin{gathered} \bf \frac{d}{dx} ( \frac{x + cosx}{tanx} ) \\ \\ = \sf \frac{tanx. \frac{d}{dx} (x + cosx) - (x + cosx) \frac{d}{dx} tanx}{ {(tanx)}^{2} } \\ ( \bf \because Quotient \: Rule ) \\ \\ = \sf\frac{tanx(1 - sinx) - (x + cosx) {sec}^{2} x}{ {tan}^{2} x} \end{gathered}
dx
d
(
tanx
x+cosx
)
=
(tanx)
2
tanx.
dx
d
(x+cosx)−(x+cosx)
dx
d
tanx
(∵QuotientRule)
=
tan
2
x
tanx(1−sinx)−(x+cosx)sec
2
x
\begin{gathered} \sf = \frac{tanx \: - \: tanx.sinx \: - \: x {sec}^{2} x \: - \: cosx. {sec}^{2} x}{ {tan}^{2}x } \\ \\ =\sf \frac{tanx \: - \: tanx.sinx \: - \: x {sec}^{2} x \: - \: cosx. \dfrac{1}{ {cos}^{2}x } }{ {tan}^{2}x } \\ \\ = \bf\frac{tanx \: - \: tanx.sinx \: - \: x {sec}^{2} x \: - \: {sec}x}{ {tan}^{2}x } \end{gathered}
=
tan
2
x
tanx−tanx.sinx−xsec
2
x−cosx.sec
2
x
=
tan
2
x
tanx−tanx.sinx−xsec
2
x−cosx.
cos
2
x
1
=
tan
2
x
tanx−tanx.sinx−xsec
2
x−secx
\large\red{ \mathfrak{ \text{W}hich \: \: is \: \text{y}our \: \: Required \: \: \text{ A}nswer }}WhichisyourRequired Answer