What is the derivative of 8^{cos(x}) ?

The derivative of 8^{cos(x}) is -3ln(2)*8^{cos(x)}sin(x)

What is the first derivative of 8^{cos(x}) ?

The first derivative of 8^{cos(x}) is -3ln(2)*8^{cos(x)}sin(x)

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\frac{d}{d x} (8^{c o s (x)})

- 3 ln (2) \cdot 8^{c o s (x)} sin (x)

Solution steps

\frac{d}{d x} (8^{c o s (x)})

Apply exponent rule:

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

8^{c o s (x)} = e^{c o s (x) l n (8)}

= \frac{d}{d x} (e^{c o s (x) l n (8)})

Apply the chain rule:

e^{c o s (x) l n (8)} \frac{d}{d x} (cos (x) ln (8))

= e^{c o s (x) l n (8)} \frac{d}{d x} (cos (x) ln (8))

\frac{d}{d x} (cos (x) ln (8)) = - 3 ln (2) sin (x)

= e^{c o s (x) l n (8)} (- 3 ln (2) sin (x))

Simplify

e^{c o s (x) l n (8)} (- 3 ln (2) sin (x)) : - 3 ln (2) \cdot 8^{c o s (x)} sin (x)

= - 3 ln (2) \cdot 8^{c o s (x)} sin (x)

f (x) = - x^{2} + 4 x, at x = 3

\int \frac{sin ( x )}{sin ( x ) + 1} d x

\frac{d X}{d X}

5 e^{- 3 (t - 2)}

y^{^{''}} - 2 y^{^{'}} + y = 2 t - 1 - (6 t e^{t} + 6 e^{t})

What is the derivative of 8^{cos(x}) ?
The derivative of 8^{cos(x}) is -3ln(2)*8^{cos(x)}sin(x)
What is the first derivative of 8^{cos(x}) ?
The first derivative of 8^{cos(x}) is -3ln(2)*8^{cos(x)}sin(x)