What is the derivative of e^{cos(x}+e^{sin(y)}) ?

The derivative of e^{cos(x}+e^{sin(y)}) is -e^{cos(x)}sin(x)+e^{sin(y)}cos(y)(dy)/(dx)

What is the first derivative of e^{cos(x}+e^{sin(y)}) ?

The first derivative of e^{cos(x}+e^{sin(y)}) is -e^{cos(x)}sin(x)+e^{sin(y)}cos(y)(dy)/(dx)

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\frac{d}{d x} (e^{c o s (x)} + e^{s i n (y)})

- e^{c o s (x)} sin (x) + e^{s i n (y)} cos (y) \frac{d y}{d x}

Solution steps

\frac{d}{d x} (e^{c o s (x)} + e^{s i n (y)})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{c o s (x)}) + \frac{d}{d x} (e^{s i n (y)})

\frac{d}{d x} (e^{c o s (x)}) = - e^{c o s (x)} sin (x)

\frac{d}{d x} (e^{s i n (y)}) = e^{s i n (y)} cos (y) \frac{d y}{d x}

= - e^{c o s (x)} sin (x) + e^{s i n (y)} cos (y) \frac{d y}{d x}

What is the derivative of e^{cos(x}+e^{sin(y)}) ?
The derivative of e^{cos(x}+e^{sin(y)}) is -e^{cos(x)}sin(x)+e^{sin(y)}cos(y)(dy)/(dx)
What is the first derivative of e^{cos(x}+e^{sin(y)}) ?
The first derivative of e^{cos(x}+e^{sin(y)}) is -e^{cos(x)}sin(x)+e^{sin(y)}cos(y)(dy)/(dx)