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

The derivative of y=cos^{ln(7x)}(x) is ((ln(cos(x)))/x-tan(x)ln(7x))(7x)^{ln(cos(x))}

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

The first derivative of y=cos^{ln(7x)}(x) is ((ln(cos(x)))/x-tan(x)ln(7x))(7x)^{ln(cos(x))}

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derivative of

y = cos^{l n (7 x)} (x)

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

\int \frac{1}{sin ( x ) - cos ( x ) - 1} d x

\int_{0}^{\frac{7}{3}} 9 + 3 x d x

\frac{\partial}{\partial x} (lo g_{e} (x^{2} + y^{2}))

\int \frac{( 5 t - t )}{3 t ^{2} - 9} d t

\frac{\partial}{\partial x} (x^{4} - 3 x^{2} y^{2} + y^{4})

What is the derivative of y=cos^{ln(7x)}(x) ?
The derivative of y=cos^{ln(7x)}(x) is ((ln(cos(x)))/x-tan(x)ln(7x))(7x)^{ln(cos(x))}
What is the first derivative of y=cos^{ln(7x)}(x) ?
The first derivative of y=cos^{ln(7x)}(x) is ((ln(cos(x)))/x-tan(x)ln(7x))(7x)^{ln(cos(x))}