Question

The function f(x) = Sin2x+cos2x+ln x+3*e to the power (x).
If the first differential of the function is
written as asin2x+bcos2x+cx+d*e to the power (X). Find the values of a,b,c and d. All answers upto o decimal.
a=
b=
с=
d=​

Answer 1

The given function is,

$\longrightarrow f(x)=\sin(2x)+\cos(2x)+\ln x+3e^x$

It's first differential is,

$\longrightarrow f(x)=2\cos(2x)-2\sin(2x)+\dfrac{1}{x}+3e^x$

$\longrightarrow f(x)=-2\sin(2x)+2\cos(2x)+\dfrac{1}{x}+3e^x\quad\quad\dots(1)$

But in the question the first differential is given as,

$\longrightarrow f(x)=a\sin(2x)+b\cos(2x)+\dfrac{c}{x}+de^x\quad\quad\dots(2)$

On comparing (1) and (2) we get,

• $\underline{\underline{a=-2}}$

• $\underline{\underline{b=2}}$

• $\underline{\underline{c=1}}$

• $\underline{\underline{d=3}}$