What is the derivative of 2^{cos^2(x)} ?

The derivative of 2^{cos^2(x)} is -ln(2)*2^{cos^2(x)}sin(2x)

What is the first derivative of 2^{cos^2(x)} ?

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

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derivative of

2^{c o s^{2} (x)}

- ln (2) \cdot 2^{c o s^{2} (x)} sin (2 x)

Solution steps

\frac{d}{d x} (2^{c o s^{2} (x)})

Apply exponent rule:

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

2^{c o s^{2} (x)} = e^{c o s^{2} (x) l n (2)}

= \frac{d}{d x} (e^{c o s^{2} (x) l n (2)})

Apply the chain rule:

e^{c o s^{2} (x) l n (2)} \frac{d}{d x} (cos^{2} (x) ln (2))

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

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

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

Simplify

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

= - ln (2) \cdot 2^{c o s^{2} (x)} sin (2 x)

4 \frac{t ^{5}}{5} - \frac{t ^{3}}{6}

\frac{d}{d q} (\frac{5 + 1}{( cot ( q ) )})

f (x) = 3 cos (x) - 4 sec (x) + 3

\frac{d}{d z} ((8 x^{3} + 3)^{4} x^{5} z^{2})

\frac{10 x + x ^{2}}{2}

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