f(x) = e^x sin x,then f^{(6)}(x) is equal to | vedclass

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

Question

(B) Given $f(x) = e^x \sin x$. First derivative: $f'(x) = e^x \sin x + e^x \cos x = e^x(\sin x + \cos x)$. Second derivative: $f''(x) = e^x(\sin x + \

Vedclass · Accepted Answer

$-8 e^x \cos x$

Vedclass · Answer

(B) Given $f(x) = e^x \sin x$. First derivative: $f'(x) = e^x \sin x + e^x \cos x = e^x(\sin x + \cos x)$. Second derivative: $f''(x) = e^x(\sin x + \cos x) + e^x(\cos x - \sin x) = 2e^x \cos x$. Third derivative: $f'''(x) = 2e^x \cos x - 2e^x \sin x = 2e^x(\cos x - \sin x)$. Fourth derivative: $f^{(4)}(x) = 2e^x(\cos x - \sin x) + 2e^x(-\sin x - \cos x) = -4e^x \sin x$. Fifth derivative: $f^{(5)}(x) = -4e^x \sin x - 4e^x \cos x = -4e^x(\sin x + \cos x)$. Sixth derivative: $f^{(6)}(x) = -4e^x(\sin x + \cos x) - 4e^x(\cos x - \sin x) = -4e^x \sin x - 4e^x \cos x - 4e^x \cos x + 4e^x \sin x = -8e^x \cos x$.

$f(x) = e^x \sin x$,then $f^{(6)}(x)$ is equal to :

Similar Questions

In the given circuit, the current flowing through it is: (in $ A$)

$DNA$ multiplication is called

Cardiac muscle fibers differ from skeletal muscle fibers in that they are -

If the vectors $\overline{AB}=3 \hat{i}+4 \hat{k}$ and $\overline{AC}=5 \hat{i}-2 \hat{j}+4 \hat{k}$ are the sides of the triangle $ABC$,then the length of the median through $A$ is

For preparing a $0.1 \, N$ solution of a compound from its impure sample,of which the percentage purity is known,the weight of the substance required will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module