What is the derivative of (4sin((nxpi/2))/(npi)) ?

The derivative of (4sin((nxpi/2))/(npi)) is 2cos((pinx)/2)

What is the first derivative of (4sin((nxpi/2))/(npi)) ?

The first derivative of (4sin((nxpi/2))/(npi)) is 2cos((pinx)/2)

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\frac{d}{d x} (\frac{4 sin ( \frac{n x π}{2} )}{nπ})

2 cos (\frac{πn x}{2})

Solution steps

\frac{d}{d x} (\frac{4 sin ( \frac{n x π}{2} )}{nπ})

Take the constant out:

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

= \frac{4}{nπ} \frac{d}{d x} (sin (\frac{n x π}{2}))

Apply the chain rule:

cos (\frac{n x π}{2}) \frac{d}{d x} (\frac{n x π}{2})

= cos (\frac{n x π}{2}) \frac{d}{d x} (\frac{n x π}{2})

\frac{d}{d x} (\frac{n x π}{2}) = \frac{πn}{2}

= \frac{4}{nπ} cos (\frac{n x π}{2}) \frac{πn}{2}

Simplify

\frac{4}{nπ} cos (\frac{n x π}{2}) \frac{πn}{2} : 2 cos (\frac{πn x}{2})

= 2 cos (\frac{πn x}{2})

\int_{0}^{\frac{π}{2}} - 1 cos^{5} (x) d x

(5.1) (9.4)

n = 1 \sum \infty \frac{2}{5 ^{n}}

(9 x + 1) y^{2} \frac{d y}{d x} + 2 x^{2} + 3 y^{3} = 0

\frac{1}{x + 3}

What is the derivative of (4sin((nxpi/2))/(npi)) ?
The derivative of (4sin((nxpi/2))/(npi)) is 2cos((pinx)/2)
What is the first derivative of (4sin((nxpi/2))/(npi)) ?
The first derivative of (4sin((nxpi/2))/(npi)) is 2cos((pinx)/2)