What is the derivative of 5^{cos(x}+ln(x^2+1)) ?

The derivative of 5^{cos(x}+ln(x^2+1)) is -ln(5)*5^{cos(x)}sin(x)+(2x)/(x^2+1)

What is the first derivative of 5^{cos(x}+ln(x^2+1)) ?

The first derivative of 5^{cos(x}+ln(x^2+1)) is -ln(5)*5^{cos(x)}sin(x)+(2x)/(x^2+1)

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\frac{d}{d x} (5^{c o s (x)} + ln (x^{2} + 1))

- ln (5) \cdot 5^{c o s (x)} sin (x) + \frac{2 x}{x ^{2} + 1}

Solution steps

\frac{d}{d x} (5^{c o s (x)} + ln (x^{2} + 1))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5^{c o s (x)}) + \frac{d}{d x} (ln (x^{2} + 1))

\frac{d}{d x} (5^{c o s (x)}) = - ln (5) \cdot 5^{c o s (x)} sin (x)

\frac{d}{d x} (ln (x^{2} + 1)) = \frac{2 x}{x ^{2} + 1}

= - ln (5) \cdot 5^{c o s (x)} sin (x) + \frac{2 x}{x ^{2} + 1}

What is the derivative of 5^{cos(x}+ln(x^2+1)) ?
The derivative of 5^{cos(x}+ln(x^2+1)) is -ln(5)*5^{cos(x)}sin(x)+(2x)/(x^2+1)
What is the first derivative of 5^{cos(x}+ln(x^2+1)) ?
The first derivative of 5^{cos(x}+ln(x^2+1)) is -ln(5)*5^{cos(x)}sin(x)+(2x)/(x^2+1)