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

The derivative of cos(x{z}(x)) is -sin(x{z}(x))({z}(x)+x derivative of {z}(x))

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

The first derivative of cos(x{z}(x)) is -sin(x{z}(x))({z}(x)+x derivative of {z}(x))

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\frac{d}{d x} (cos (x z (x)))

- sin (x z (x)) (z (x) + x \frac{d}{d x} (z (x)))

Solution steps

\frac{d}{d x} (cos (x z (x)))

Apply the chain rule:

- sin (x z (x)) \frac{d}{d x} (x z (x))

= - sin (x z (x)) \frac{d}{d x} (x z (x))

\frac{d}{d x} (x z (x)) = z (x) + x \frac{d}{d x} (z (x))

= - sin (x z (x)) (z (x) + x \frac{d}{d x} (z (x)))

\int x^{\frac{4}{3}} - 3 x^{\frac{5}{2}} d x

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

\int_{0}^{2} 4 - x^{2} d x

\frac{d}{d t} (1 + 2 t)

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

What is the derivative of cos(x{z}(x)) ?
The derivative of cos(x{z}(x)) is -sin(x{z}(x))({z}(x)+x derivative of {z}(x))
What is the first derivative of cos(x{z}(x)) ?
The first derivative of cos(x{z}(x)) is -sin(x{z}(x))({z}(x)+x derivative of {z}(x))