What is the derivative of 4^{sin(x)} ?

The derivative of 4^{sin(x)} is ln(2)*2^{2sin(x)+1}cos(x)

What is the first derivative of 4^{sin(x)} ?

The first derivative of 4^{sin(x)} is ln(2)*2^{2sin(x)+1}cos(x)

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derivative of

4^{s i n (x)}

ln (2) \cdot 2^{2 s i n (x) + 1} cos (x)

Solution steps

\frac{d}{d x} (4^{s i n (x)})

Apply exponent rule:

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

4^{s i n (x)} = e^{s i n (x) l n (4)}

= \frac{d}{d x} (e^{s i n (x) l n (4)})

Apply the chain rule:

e^{s i n (x) l n (4)} \frac{d}{d x} (sin (x) ln (4))

= e^{s i n (x) l n (4)} \frac{d}{d x} (sin (x) ln (4))

\frac{d}{d x} (sin (x) ln (4)) = 2 ln (2) cos (x)

= e^{s i n (x) l n (4)} \cdot 2 ln (2) cos (x)

Simplify

e^{s i n (x) l n (4)} \cdot 2 ln (2) cos (x) : ln (2) \cdot 2^{2 s i n (x) + 1} cos (x)

= ln (2) \cdot 2^{2 s i n (x) + 1} cos (x)

sin (2 x) d x + cos (7 y) d y = 0, y (π^{2}) = π^{7}

\frac{d}{d x} (\frac{x}{5})

\frac{\partial}{\partial x} (y - x)

y^{^{''}} + 16 y = 8 sin (4 x)

x \to 0 lim (\frac{x}{tan ( 3 x )})

What is the derivative of 4^{sin(x)} ?
The derivative of 4^{sin(x)} is ln(2)*2^{2sin(x)+1}cos(x)
What is the first derivative of 4^{sin(x)} ?
The first derivative of 4^{sin(x)} is ln(2)*2^{2sin(x)+1}cos(x)