What is the derivative of sin({p}(x)ix) ?

The derivative of sin({p}(x)ix) is i(sin({p}(x))+xcos({p}(x)) derivative of {p}(x))

What is the first derivative of sin({p}(x)ix) ?

The first derivative of sin({p}(x)ix) is i(sin({p}(x))+xcos({p}(x)) derivative of {p}(x))

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\frac{d}{d x} (sin (p (x)) i x)

i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))

Solution steps

\frac{d}{d x} (sin (p (x)) i x)

Take the constant out:

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

= i \frac{d}{d x} (sin (p (x)) x)

Apply the Product Rule:

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

f = sin (p (x)), g = x

= i (\frac{d}{d x} (sin (p (x))) x + \frac{d x}{d x} sin (p (x)))

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

\frac{d x}{d x} = 1

= i (cos (p (x)) \frac{d}{d x} (p (x)) x + 1 \cdot sin (p (x)))

Simplify

i (cos (p (x)) \frac{d}{d x} (p (x)) x + 1 \cdot sin (p (x))) : i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))

= i (sin (p (x)) + x cos (p (x)) \frac{d}{d x} (p (x)))

cos (8 x)

\frac{s}{( s - 3 ) ^{2}}

\int (x^{2} + x)^{13} (2 x + 1) d x

\int (t)^{\frac{1}{2}} d t

\int tan (6 x) (sec (6 x))^{2} d x

What is the derivative of sin({p}(x)ix) ?
The derivative of sin({p}(x)ix) is i(sin({p}(x))+xcos({p}(x)) derivative of {p}(x))
What is the first derivative of sin({p}(x)ix) ?
The first derivative of sin({p}(x)ix) is i(sin({p}(x))+xcos({p}(x)) derivative of {p}(x))