What is the derivative of sin(1-xcos^3(x)) ?

The derivative of sin(1-xcos^3(x)) is -cos^3(x)cos(1-x)-3cos^2(x)sin(x)sin(1-x)

What is the first derivative of sin(1-xcos^3(x)) ?

The first derivative of sin(1-xcos^3(x)) is -cos^3(x)cos(1-x)-3cos^2(x)sin(x)sin(1-x)

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\frac{d}{d x} (sin (1 - x) cos^{3} (x))

- cos^{3} (x) cos (1 - x) - 3 cos^{2} (x) sin (x) sin (1 - x)

Solution steps

\frac{d}{d x} (sin (1 - x) cos^{3} (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (1 - x), g = cos^{3} (x)

= \frac{d}{d x} (sin (1 - x)) cos^{3} (x) + \frac{d}{d x} (cos^{3} (x)) sin (1 - x)

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

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

= (- cos (1 - x)) cos^{3} (x) + (- 3 cos^{2} (x) sin (x)) sin (1 - x)

Simplify

= - cos^{3} (x) cos (1 - x) - 3 cos^{2} (x) sin (x) sin (1 - x)

f (x) = \frac{e ^{x}}{2 + 5 x}

x + \frac{y d y}{d x} = 0

6 y^{^{'}} - 2 y = x y^{4}, y (0) = - 2

f (x) = \frac{6 x + 16}{x + 3}

\frac{d}{d x} (x x + x^{2} x)

What is the derivative of sin(1-xcos^3(x)) ?
The derivative of sin(1-xcos^3(x)) is -cos^3(x)cos(1-x)-3cos^2(x)sin(x)sin(1-x)
What is the first derivative of sin(1-xcos^3(x)) ?
The first derivative of sin(1-xcos^3(x)) is -cos^3(x)cos(1-x)-3cos^2(x)sin(x)sin(1-x)