What is the derivative of 5^{cos(x}) ?

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

What is the first derivative of 5^{cos(x}) ?

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

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\frac{d}{d x} (5^{c o s (x)})

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

Solution steps

\frac{d}{d x} (5^{c o s (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

5^{c o s (x)} = e^{c o s (x) l n (5)}

= \frac{d}{d x} (e^{c o s (x) l n (5)})

Apply the chain rule:

e^{c o s (x) l n (5)} \frac{d}{d x} (cos (x) ln (5))

= e^{c o s (x) l n (5)} \frac{d}{d x} (cos (x) ln (5))

\frac{d}{d x} (cos (x) ln (5)) = - ln (5) sin (x)

= e^{c o s (x) l n (5)} (- ln (5) sin (x))

Simplify

e^{c o s (x) l n (5)} (- ln (5) sin (x)) : - ln (5) \cdot 5^{c o s (x)} sin (x)

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

\frac{d}{d x} ((3 x^{2} - 2 x)^{3})

x \to \frac{8}{9} lim (x^{4})

f (t) = 5 cos (t)

\frac{d y}{d x} = 8 x (6 y + 5)^{\frac{1}{2}}

\int \frac{- 38 y + 25}{- y ( 7 y - 5 )} d y

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