We wish everyone a good day. In this article, we will tell you what the integral of tan(x) is.
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| integral of tanx |
The integral of tanx is -ln|cos(x)|
$\int{tan(x)dx}=-ln|cos(x)|$
Tangent(x) integral ==> $-ln|cos(x)|+C$
Thank you and good work.
One of the most curious questions about its integral is cosx. We will briefly explain what the integral of cosx is for you.
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| integral of cosx |
The integral of cosx is sinx.
$\int{cos(x)dx}=sin(x)$
If you memorize the graph above, you can solve sinx and cosx derivatives and integrals correctly without any confusion. Thanks.
We wish everyone a good day. In this lesson, we will share with you what is the graph of e to the x.
e = 2.718281828459045235360287471352662497757247……. continues in the form.
The number e is an infinite number like the number π. It is commonly known as e=2.718
Also, Euler formulas = $e^{(iθ)}=cos(θ)+isin(θ)$
The graph plot of e to the x is as follows:
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| e x graph |
Thank you so much. We wish you success in your studies.
Warning = When you give -1 to x in the graph of e to the x, it may seem like it comes out 0. But when it takes the value of x=-1, it gives the value of 1/e, that is, 1/2.718. If you noticed on the chart, it should be equal to a value below 0.5. So 0.5 in the y part of the graph is given a little below. Normally it should be above. But in general, the graph is correct.
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| ex graph |
From the picture above, you can find another e to the x graph.
Hello dear friends. In this lesson, we will tell you step by step what is the derivative of x.lnx.
First, let's write the product derivative formula:
Firstl, we can let $y=f(x).g(x)$
So derivate of $y’=f(x)’.g(x)+g(x)’.f(x)$
Now, we can go our solution, derivative of x.ln(x)
So, while taking the derivative of x.lnx, we take the derivative of the 1st and multiply it by the 2nd. Then we take the derivative of the 2nd and multiply it by the 1st. Then we add the two. Thus, we find its derivative. Now let's do it step by step.
Let $y=x.ln(x)$
x.lnx Derivative:
1-) $y’=x'.ln(x)+ln'(x).x$
2-) $y'=1.ln(x)+\frac{1}{x}.x$
3-) $y'=ln(x)+1$
4-) As a result, our answer is lnx+1
x.lnx derivative = ln(x)+1
Thank you so much...
