What is the derivative of pi\sqrt[5]{x}cos(x) ?

The derivative of pi\sqrt[5]{x}cos(x) is pi((cos(x))/(5x^{4/5)}-\sqrt[5]{x}sin(x))

What is the first derivative of pi\sqrt[5]{x}cos(x) ?

The first derivative of pi\sqrt[5]{x}cos(x) is pi((cos(x))/(5x^{4/5)}-\sqrt[5]{x}sin(x))

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\frac{d}{d x} (π 5 x cos (x))

π (\frac{cos ( x )}{5 x ^{\frac{4}{5}}} - 5 x sin (x))

Solution steps

\frac{d}{d x} (π 5 x cos (x))

Take the constant out:

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

= π \frac{d}{d x} (5 x cos (x))

Apply the Product Rule:

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

f = 5 x, g = cos (x)

= π (\frac{d}{d x} (5 x) cos (x) + \frac{d}{d x} (cos (x)) 5 x)

\frac{d}{d x} (5 x) = \frac{1}{5 x ^{\frac{4}{5}}}

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

= π (\frac{1}{5 x ^{\frac{4}{5}}} cos (x) + (- sin (x)) 5 x)

Simplify

π (\frac{1}{5 x ^{\frac{4}{5}}} cos (x) + (- sin (x)) 5 x) : π (\frac{cos ( x )}{5 x ^{\frac{4}{5}}} - 5 x sin (x))

= π (\frac{cos ( x )}{5 x ^{\frac{4}{5}}} - 5 x sin (x))

\frac{d}{d x} (C e^{x})

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

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

\int (cos^{2} (x) \cdot sin (x)) d x

\int \frac{12 x ^{3}}{x ^{4} + 7} d x

What is the derivative of pi\sqrt[5]{x}cos(x) ?
The derivative of pi\sqrt[5]{x}cos(x) is pi((cos(x))/(5x^{4/5)}-\sqrt[5]{x}sin(x))
What is the first derivative of pi\sqrt[5]{x}cos(x) ?
The first derivative of pi\sqrt[5]{x}cos(x) is pi((cos(x))/(5x^{4/5)}-\sqrt[5]{x}sin(x))