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

The derivative of a^{sqrt(cos(x)}) is -(a^{sqrt(cos(x))}ln(a)sin(x))/(2sqrt(cos(x)))

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

The first derivative of a^{sqrt(cos(x)}) is -(a^{sqrt(cos(x))}ln(a)sin(x))/(2sqrt(cos(x)))

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

- \frac{a ^{c o s (x)} ln ( a ) sin ( x )}{2 cos ( x )}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

= e^{c o s (x) l n (a)} (- \frac{ln ( a ) sin ( x )}{2 cos ( x )})

Simplify

e^{c o s (x) l n (a)} (- \frac{ln ( a ) sin ( x )}{2 cos ( x )}) : - \frac{a ^{c o s (x)} ln ( a ) sin ( x )}{2 cos ( x )}

= - \frac{a ^{c o s (x)} ln ( a ) sin ( x )}{2 cos ( x )}

\int \frac{u + 1}{u ^{2} + 1} d u

f (x) = cos^{4} (sin^{3} (x))

f (x) = x^{4} + 7 x^{2} - x, at x = 1

\frac{( x ^{2} + 1 )}{( x + 1 )}, 1

\frac{\partial}{\partial u} (u - uv)

What is the derivative of a^{sqrt(cos(x)}) ?
The derivative of a^{sqrt(cos(x)}) is -(a^{sqrt(cos(x))}ln(a)sin(x))/(2sqrt(cos(x)))
What is the first derivative of a^{sqrt(cos(x)}) ?
The first derivative of a^{sqrt(cos(x)}) is -(a^{sqrt(cos(x))}ln(a)sin(x))/(2sqrt(cos(x)))