What is the derivative of 7^{cos(x}) ?

The derivative of 7^{cos(x}) is -ln(7)*7^{cos(x)}sin(x)

What is the first derivative of 7^{cos(x}) ?

The first derivative of 7^{cos(x}) is -ln(7)*7^{cos(x)}sin(x)

Popular >

\frac{d}{d x} (7^{c o s (x)})

- ln (7) \cdot 7^{c o s (x)} sin (x)

Solution steps

\frac{d}{d x} (7^{c o s (x)})

Apply exponent rule:

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

7^{c o s (x)} = e^{c o s (x) l n (7)}

= \frac{d}{d x} (e^{c o s (x) l n (7)})

Apply the chain rule:

e^{c o s (x) l n (7)} \frac{d}{d x} (cos (x) ln (7))

= e^{c o s (x) l n (7)} \frac{d}{d x} (cos (x) ln (7))

\frac{d}{d x} (cos (x) ln (7)) = - ln (7) sin (x)

= e^{c o s (x) l n (7)} (- ln (7) sin (x))

Simplify

e^{c o s (x) l n (7)} (- ln (7) sin (x)) : - ln (7) \cdot 7^{c o s (x)} sin (x)

= - ln (7) \cdot 7^{c o s (x)} sin (x)

\frac{d}{d x} (x^{2} arctan (4 x))

y^{^{''}} + 8 y^{^{'}} + 15 y = 0, y (0) = 0, y^{^{'}} (0) = 0

(x, y) \to (0, 0) lim (x + y)

\int \frac{3}{1 + e ^{2 x}} d x

\int_{0}^{1} x^{7} (1 + x^{8})^{7} d x

What is the derivative of 7^{cos(x}) ?
The derivative of 7^{cos(x}) is -ln(7)*7^{cos(x)}sin(x)
What is the first derivative of 7^{cos(x}) ?
The first derivative of 7^{cos(x}) is -ln(7)*7^{cos(x)}sin(x)