What is the derivative of {f}(x+{g}(x)) ?

The derivative of {f}(x+{g}(x)) is derivative of {f}(x)+derivative of {g}(x)

What is the first derivative of {f}(x+{g}(x)) ?

The first derivative of {f}(x+{g}(x)) is derivative of {f}(x)+derivative of {g}(x)

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\frac{d}{d x} (f (x) + g (x))

\frac{d}{d x} (f (x)) + \frac{d}{d x} (g (x))

Solution steps

\frac{d}{d x} (f (x) + g (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (f (x)) + \frac{d}{d x} (g (x))

= \frac{d}{d x} (f (x)) + \frac{d}{d x} (g (x))

\frac{d}{d x} (x^{m})

y^{^{''}} + 8 y^{^{'}} + 15 y = 0

f (x) = \frac{2 x}{9 x ^{2} + 1}

\int_{4}^{7} x^{2} d x

\int y^{3} e^{y^{2}} d y

What is the derivative of {f}(x+{g}(x)) ?
The derivative of {f}(x+{g}(x)) is derivative of {f}(x)+derivative of {g}(x)
What is the first derivative of {f}(x+{g}(x)) ?
The first derivative of {f}(x+{g}(x)) is derivative of {f}(x)+derivative of {g}(x)