What is the derivative of e^xcos(y+x) ?

The derivative of e^xcos(y+x) is e^xcos(y)-e^xsin(y)(dy)/(dx)+1

What is the first derivative of e^xcos(y+x) ?

The first derivative of e^xcos(y+x) is e^xcos(y)-e^xsin(y)(dy)/(dx)+1

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

e^{x} cos (y) - e^{x} sin (y) \frac{d y}{d x} + 1

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= e^{x} cos (y) - e^{x} sin (y) \frac{d y}{d x} + 1

f (x) = 5 x + e^{3 x} ln (x)

(x^{2} + 3 x)^{2}

\int (3 x^{2} + 4 x) d x

y = x - 1, y = 0, x = 7

x \to \infty lim (e^{x} - 1)

What is the derivative of e^xcos(y+x) ?
The derivative of e^xcos(y+x) is e^xcos(y)-e^xsin(y)(dy)/(dx)+1
What is the first derivative of e^xcos(y+x) ?
The first derivative of e^xcos(y+x) is e^xcos(y)-e^xsin(y)(dy)/(dx)+1