What is the derivative of e^{{p}(t,xt}*cos(nt)) ?

The derivative of e^{{p}(t,xt}*cos(nt)) is cos(nt)e^{{p}(t,x)t}t derivative of {p}(t,x)

What is the first derivative of e^{{p}(t,xt}*cos(nt)) ?

The first derivative of e^{{p}(t,xt}*cos(nt)) is cos(nt)e^{{p}(t,x)t}t derivative of {p}(t,x)

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\frac{d}{d x} (e^{p (t, x) t} \cdot cos (n t))

cos (n t) e^{p (t, x) t} t \frac{d}{d x} (p (t, x))

Solution steps

\frac{d}{d x} (e^{p (t, x) t} cos (n t))

Treat

n, t

as a constant

Take the constant out:

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

= cos (n t) \frac{d}{d x} (e^{p (t, x) t})

Apply the chain rule:

e^{p (t, x) t} \frac{d}{d x} (p (t, x) t)

= e^{p (t, x) t} \frac{d}{d x} (p (t, x) t)

\frac{d}{d x} (p (t, x) t) = t \frac{d}{d x} (p (t, x))

= cos (n t) e^{p (t, x) t} t \frac{d}{d x} (p (t, x))

\frac{\partial}{\partial x} (6 - x^{2} + 2 y^{2})

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

\int \frac{x + 3}{x ^{2} - 2 x - 3} d x

\int f (x + b) d x

x + 2

What is the derivative of e^{{p}(t,xt}*cos(nt)) ?
The derivative of e^{{p}(t,xt}*cos(nt)) is cos(nt)e^{{p}(t,x)t}t derivative of {p}(t,x)
What is the first derivative of e^{{p}(t,xt}*cos(nt)) ?
The first derivative of e^{{p}(t,xt}*cos(nt)) is cos(nt)e^{{p}(t,x)t}t derivative of {p}(t,x)