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Differentiation — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferentiation3 Marks
Question
Diffrentiate the following w.r.t.x

$y=(25)^{\log _5(\sec x)}-(16)^{\log _4(\tan x)}$

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Answer

$\begin{aligned} & y=(25)^{\log _5(\sec x)}-(16)^{\log _4(\tan x)} \\ & =5^{2 \log _5(\sec x)}-4^{2 \log _4(\tan x)} \\ & =5^{\log _5(\sec 5 x)}-4^{\log _4(\tan 2 x)} \\ & =\sec ^2 x-\tan ^2 x \ldots[\because=x] \\ & \therefore y=1\end{aligned}$

Differentiating w.r.t. x, we get

$\frac{d y}{d x}=\frac{d}{d x}(1)=0$

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