What is the derivative of f(x)=5^{sin(x)} ?

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

What is the first derivative of f(x)=5^{sin(x)} ?

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

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derivative of

f (x) = 5^{s i n (x)}

ln (5) \cdot 5^{s i n (x)} cos (x)

Solution steps

\frac{d}{d x} (5^{s i n (x)})

Apply exponent rule:

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

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

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

Apply the chain rule:

e^{s i n (x) l n (5)} \frac{d}{d x} (sin (x) ln (5))

= e^{s i n (x) l n (5)} \frac{d}{d x} (sin (x) ln (5))

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

= e^{s i n (x) l n (5)} ln (5) cos (x)

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

= ln (5) \cdot 5^{s i n (x)} cos (x)

\int_{1}^{e} ln (11 x) d x

\int 5^{x^{2}} d x

\int \frac{x}{36 - x ^{2}} d x

\int \frac{5 x ^{3} + 5 x}{x - 1} d x

y^{^{'}} + y = e^{t} + 11

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