How do you find the derivative of $y = e^{x} (sin x + cos x)$ $y=e^x(sinx+cosx)$ ?

Question

How do you find the derivative of $y = e^{x} (sin x + cos x)$ $y=e^x(sinx+cosx)$ ?

1 Answer

Impact of this question

41936 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-25T09:25:12

$\frac{d y}{d x} = 2 e^{x} cos x$ $dy/dx=2e^xcosx$

Explanation:

differentiate using the $product rule$ $color(blue)"product rule"$

$Given y = g (x) . h (x) then$ $"Given "y=g(x).h(x)" then"$

$color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=g(x)h'(x)+h(x)g'(x))color(white)(2/2)|)))$

$"here "g(x)=e^xrArrg'(x)=e^x$

$"and "h(x)=sinx+cosxrArrg'(x)=cosx-sinx$

$rArrdy/dx=e^x(cosx-sinx)+e^x(sinx+cosx)$

$color(white)(xxxxx)=e^xcosxcancel(-e^xsinx)cancel(e^xsinx)+e^xcosx$

$color(white)(xxxxx)=2e^xcosx$

Science

Math

Humanities

... and beyond

How do you find the derivative of $y = e^{x} (sin x + cos x)$ $y=e^x(sinx+cosx)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the derivative of y=e^x(sinx+cosx)y=ex(sinx+cosx)y=e^x(sinx+cosx)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the derivative of $y = e^{x} (sin x + cos x)$ $y=e^x(sinx+cosx)$ ?