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Popular >

derivative of 5^{sin(x})

Solution

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

Solution

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)

Graph

Popular Examples

derivative of x^2cos^2(x)

\frac{d}{d x} (x^{2} cos^{2} (x))

\frac{d y}{d t} = 2 t

derivative of (e^{2x}/(x-3))

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

(dy)/(dt)=e^{-3t},y(0)=10

\frac{d y}{d t} = e^{- 3 t}, y (0) = 10

derivative of (x-1)^2(2x+1)^4 derivative of

(x - 1)^{2} (2 x + 1)^{4}

Frequently Asked Questions (FAQ)

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