Nth Derivative Of e2xSin3x.Sin2xe2xSin3x.Sin2x<script type="math/asciimath" id="MathJax-Element-1">e^{2x} Sin3x.Sin2x</script> | Leibnitz Theorem Of Nth Derivatives Examples

To Find n_th derivative of e^(2x) Sin3x Sin2x

In this quick tutorial we will learn how to find n_th derivative of a function which is in the form of e^ax. sinbx. sincx. So let us understand steps to reach n_th derivative very carefully.

Solution: let u = $e^(2x)$ and v = $Sin3x .Sin2x$

Since we know that:

$SinA.SinB$ = $\frac{1}{2}$ {cos(A-B) - cos(A+B)}

Now let: A = 3X And B = 2X

Therefore,

$(A-B)$ =

$X$ and

$(A+B)$ =

$5X$

Also

$y = e^{x}.\frac{1}{2}.{cos(A-B) - cos(A+B)}$

$y = \frac{1}{2}.{e^{x}.cosX - e^{x}.cos5X}$

$N_th$ derivative of

$e^{Ax}.Cos(Bx+c)$ is:

$(A^{2}+B^{2})^{n/2}.e^{Ax}.Cos(Bx+C+n.tan^{-1}\frac{B}{A})$

$n_th$ derivative of

$\frac{1}{2}.[e^{2x}.CosX\]$ is:

$\frac{1}{2}.(2^{2}+1^{2})^{n/2}. e^{2x}. Cos(X+n.tan^{-1}\frac{1}{2})$

$\frac{1}{2}.5^{2}. e^{2x}.Cos(X+n.tan^{-1}\frac{1}{2})$

Similarly

$n_th$ derivative of

$e^{2x}.Cos5X$ as:

$\frac{1}{2}.29^{n/2}. e^{2x}.Cos(5X+n.tan^{-1}\frac{5}{2})$

Finally $N_th$ derivative of $e^(2x) Sin3x Sin2x$ is:

$\frac{1}{2}.5^{2}. e^{2x}.Cos(X+n.tan^{-1}\frac{1}{2})$ -

$\frac{1}{2}.29^{n/2}. e^{2x}.Cos(5X+n.tan^{-1}\frac{5}{2})$

$Nth Derivative Of `e^{2x} Sin3x.Sin2x`$

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Nth Derivative Of $e^{2x} Sin3x.Sin2x$ | Leibnitz Theorem Of Nth Derivatives Examples

To Find n_th derivative of e^(2x) Sin3x Sin2x

$SinA.SinB$ = $\frac{1}{2}$ {cos(A-B) - cos(A+B)}

Finally $N_th$ derivative of $e^(2x) Sin3x Sin2x$ is:

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Nth Derivative Of e2xSin3x.Sin2xe^{2x} Sin3x.Sin2x | Leibnitz Theorem Of Nth Derivatives Examples

To Find n_th derivative of e^(2x) Sin3x Sin2x

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Finally NthN_th derivative of e2xSin3xSin2xe^(2x) Sin3x Sin2x is:

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No comments:

Post a Comment

Translate This Website

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Contact Form

Labels

Nth Derivative Of $e^{2x} Sin3x.Sin2x$ | Leibnitz Theorem Of Nth Derivatives Examples

$SinA.SinB$ = $\frac{1}{2}$ {cos(A-B) - cos(A+B)}

Finally $N_th$ derivative of $e^(2x) Sin3x Sin2x$ is:

Nth Derivative Of $e^{2x} Sin3x.Sin2x$ | Leibnitz Theorem Of Nth Derivatives ExamplesJan 10, 2021