What is the d/(d{x)}(cos^3({x})cos^4({y})cos^5({z})) ?

The d/(d{x)}(cos^3({x})cos^4({y})cos^5({z})) is -3cos^5({z})cos^4({y})cos^2({x})sin({x})

What is the first d/(d{x)}(cos^3({x})cos^4({y})cos^5({z})) ?

The first d/(d{x)}(cos^3({x})cos^4({y})cos^5({z})) is -3cos^5({z})cos^4({y})cos^2({x})sin({x})

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\frac{d}{d x} (cos^{3} (x) cos^{4} (y) cos^{5} (z))

- 3 cos^{5} (z) cos^{4} (y) cos^{2} (x) sin (x)

Solution steps

\frac{d}{d x} (cos^{3} (x) cos^{4} (y) cos^{5} (z))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= cos^{4} (y) cos^{5} (z) \frac{d}{d x} (cos^{3} (x))

Apply the chain rule:

3 (cos (x))^{2} \frac{d}{d x} (cos (x))

= 3 (cos (x))^{2} \frac{d}{d x} (cos (x))

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

= cos^{4} (y) cos^{5} (z) \cdot 3 (cos (x))^{2} (- sin (x))

Simplify

= - 3 cos^{5} (z) cos^{4} (y) cos^{2} (x) sin (x)

\frac{x ^{3}}{4 - x}

\frac{1}{4 x ^{2}}

f (x) = 50

y = x (4 x - 3)

\frac{d}{d t} (- 10 + 2.5 t)

What is the d/(d{x)}(cos^3({x})cos^4({y})cos^5({z})) ?
The d/(d{x)}(cos^3({x})cos^4({y})cos^5({z})) is -3cos^5({z})cos^4({y})cos^2({x})sin({x})
What is the first d/(d{x)}(cos^3({x})cos^4({y})cos^5({z})) ?
The first d/(d{x)}(cos^3({x})cos^4({y})cos^5({z})) is -3cos^5({z})cos^4({y})cos^2({x})sin({x})