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

The derivative of (cos(7x)^x) is cos^x(7x)(ln(cos(7x))-7xtan(7x))

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

The first derivative of (cos(7x)^x) is cos^x(7x)(ln(cos(7x))-7xtan(7x))

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\frac{d}{d x} ((cos (7 x))^{x})

cos^{x} (7 x) (ln (cos (7 x)) - 7 x tan (7 x))

Solution steps

\frac{d}{d x} ((cos (7 x))^{x})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

= cos^{x} (7 x) (ln (cos (7 x)) - 7 x tan (7 x))

x, \frac{1}{2} x, 0, 25

\frac{\partial}{\partial x} (\frac{3 x - y}{3 x + y})

\int x (2 x - 1)^{9} d x

f (x) = x^{2} - 9, (4, 7)

What is the derivative of (cos(7x)^x) ?
The derivative of (cos(7x)^x) is cos^x(7x)(ln(cos(7x))-7xtan(7x))
What is the first derivative of (cos(7x)^x) ?
The first derivative of (cos(7x)^x) is cos^x(7x)(ln(cos(7x))-7xtan(7x))