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

The derivative of e^{cos(x+ln(x)}) is -e^{cos(x)}xsin(x)+e^{cos(x)}

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

The first derivative of e^{cos(x+ln(x)}) is -e^{cos(x)}xsin(x)+e^{cos(x)}

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

- e^{c o s (x)} x sin (x) + e^{c o s (x)}

Solution steps

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

Simplify

e^{c o s (x) + l n (x)} : e^{c o s (x)} x

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

Apply the Product Rule:

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

f = e^{c o s (x)}, g = x

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

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

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

= (- e^{c o s (x)} sin (x)) x + 1 \cdot e^{c o s (x)}

Simplify

= - e^{c o s (x)} x sin (x) + e^{c o s (x)}

What is the derivative of e^{cos(x+ln(x)}) ?
The derivative of e^{cos(x+ln(x)}) is -e^{cos(x)}xsin(x)+e^{cos(x)}
What is the first derivative of e^{cos(x+ln(x)}) ?
The first derivative of e^{cos(x+ln(x)}) is -e^{cos(x)}xsin(x)+e^{cos(x)}