What is the derivative of (t(e^t(sin(t)+cos(t)))) ?

The derivative of (t(e^t(sin(t)+cos(t)))) is e^x(sin(x)+cos(x))+2e^xxcos(x)

What is the first derivative of (t(e^t(sin(t)+cos(t)))) ?

The first derivative of (t(e^t(sin(t)+cos(t)))) is e^x(sin(x)+cos(x))+2e^xxcos(x)

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Popular >

\frac{d}{d x} ((x) (e^{x} (sin (x) + cos (x))))

e^{x} (sin (x) + cos (x)) + 2 e^{x} x cos (x)

Solution steps

\frac{d}{d x} ((x) (e^{x} (sin (x) + cos (x))))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x} (sin (x) + cos (x))

= \frac{d x}{d x} e^{x} (sin (x) + cos (x)) + \frac{d}{d x} (e^{x} (sin (x) + cos (x))) x

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{x} (sin (x) + cos (x))) = 2 e^{x} cos (x)

= 1 \cdot e^{x} (sin (x) + cos (x)) + 2 e^{x} cos (x) x

Simplify

= e^{x} (sin (x) + cos (x)) + 2 e^{x} x cos (x)

\frac{1 + 10}{2}

(x - \frac{1}{4}) (x - (-) \frac{2}{3})

x + 3 2^{2}

\frac{( x + 1 ) ^{2}}{x - 1}

2 (x - 3 y)

What is the derivative of (t(e^t(sin(t)+cos(t)))) ?
The derivative of (t(e^t(sin(t)+cos(t)))) is e^x(sin(x)+cos(x))+2e^xxcos(x)
What is the first derivative of (t(e^t(sin(t)+cos(t)))) ?
The first derivative of (t(e^t(sin(t)+cos(t)))) is e^x(sin(x)+cos(x))+2e^xxcos(x)