If 3 f(cos x) + 2 f(sin x) = 5 x,then f^{prim | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given: $3 f(\cos x) + 2 f(\sin x) = 5 x$  ...$(i)$Replace $x$ with $(\frac{\pi}{2} - x)$:$3 f(\sin x) + 2 f(\cos x) = 5(\frac{\pi}{2} - x)$  ...$(

Vedclass · Accepted Answer

$\frac{-5}{\sin x} - \frac{5}{\cos x}$

Vedclass · Answer

(C) Given: $3 f(\cos x) + 2 f(\sin x) = 5 x$  ...$(i)$Replace $x$ with $(\frac{\pi}{2} - x)$:$3 f(\sin x) + 2 f(\cos x) = 5(\frac{\pi}{2} - x)$  ...$(ii)$Multiply $(i)$ by $3$ and $(ii)$ by $2$:$9 f(\cos x) + 6 f(\sin x) = 15 x$$4 f(\cos x) + 6 f(\sin x) = 10(\frac{\pi}{2} - x) = 5\pi - 10 x$Subtracting the equations:$5 f(\cos x) = 25 x - 5\pi \Rightarrow f(\cos x) = 5 x - \pi$Differentiating with respect to $x$:$f^{\prime}(\cos x) \cdot (-\sin x) = 5 \Rightarrow f^{\prime}(\cos x) = \frac{-5}{\sin x}$Similarly,from $(i)$ and $(ii)$,we find $f(\sin x) = \frac{5\pi}{2} - 5x$:$f^{\prime}(\sin x) \cdot (\cos x) = -5 \Rightarrow f^{\prime}(\sin x) = \frac{-5}{\cos x}$Therefore,$f^{\prime}(\cos x) + f^{\prime}(\sin x) = \frac{-5}{\sin x} - \frac{5}{\cos x}$.

If $3 f(\cos x) + 2 f(\sin x) = 5 x$,then $f^{\prime}(\cos x) + f^{\prime}(\sin x) =$

Similar Questions

If $\log _{10}\left(\frac{x^3-y^3}{x^3+y^3}\right)=2$,then $\frac{d y}{d x}=$

For $x>1$,if $(2 x)^{2 y}=4 e^{2 x-2 y}$,then $(1+\log 2 x)^2 \frac{d y}{d x}$ is equal to

If $y = \sqrt{\log x + \sqrt{\log x + \sqrt{\log x + \dots \infty}}}$,then $\frac{dy}{dx} = $

Find $\frac{dy}{dx}$,if $x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}$.

If $y = \sqrt{\cos x^2 + \sqrt{\cos x^2 + \sqrt{\cos x^2 + \dots \infty}}}$ and $\frac{dy}{dx} = \frac{f(x)}{2y - 1}$, then $\int f(x) dx = \dots$

Vedclass Test Series

Exam Paper Generator

Online Exam Module