What is the derivative of ce^{5t}+ce^{5{y}(t,x}) ?

The derivative of ce^{5t}+ce^{5{y}(t,x}) is 0+ce^{5{y}(t,x)}*5 derivative of {y}(t,x)

What is the first derivative of ce^{5t}+ce^{5{y}(t,x}) ?

The first derivative of ce^{5t}+ce^{5{y}(t,x}) is 0+ce^{5{y}(t,x)}*5 derivative of {y}(t,x)

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\frac{d}{d x} (c e^{5 t} + c e^{5 y (t, x)})

0 + c e^{5 y (t, x)} \cdot 5 \frac{d}{d x} (y (t, x))

Solution steps

\frac{d}{d x} (c e^{5 t} + c e^{5 y (t, x)})

Treat

c, t

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (c e^{5 t}) + \frac{d}{d x} (c e^{5 y (t, x)})

\frac{d}{d x} (c e^{5 t}) = 0

\frac{d}{d x} (c e^{5 y (t, x)}) = c e^{5 y (t, x)} \cdot 5 \frac{d}{d x} (y (t, x))

= 0 + c e^{5 y (t, x)} \cdot 5 \frac{d}{d x} (y (t, x))

\int_{4.5}^{5} \frac{x}{8} d x

\frac{1}{4} y^{^{''}} + y^{^{'}} + y = x^{2} - 2 x

\frac{d y}{d x} = - 10 x^{4} y

x \to 0 + lim (cos^{x} (\frac{π}{2} - x))

\int 5 cos (2 x) d x

What is the derivative of ce^{5t}+ce^{5{y}(t,x}) ?
The derivative of ce^{5t}+ce^{5{y}(t,x}) is 0+ce^{5{y}(t,x)}*5 derivative of {y}(t,x)
What is the first derivative of ce^{5t}+ce^{5{y}(t,x}) ?
The first derivative of ce^{5t}+ce^{5{y}(t,x}) is 0+ce^{5{y}(t,x)}*5 derivative of {y}(t,x)