What is the derivative of {g}(h,x(h(x))) ?

The derivative of {g}(h,x(h(x))) is h(derivative of {g}(h,x)x+1*{g}(h,x))

What is the first derivative of {g}(h,x(h(x))) ?

The first derivative of {g}(h,x(h(x))) is h(derivative of {g}(h,x)x+1*{g}(h,x))

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\frac{d}{d x} (g (h, x) (h (x)))

h (\frac{d}{d x} (g (h, x)) x + 1 \cdot g (h, x))

Solution steps

\frac{d}{d x} (g (h, x) (h (x)))

Treat

h

as a constant

Take the constant out:

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

= h \frac{d}{d x} (g (h, x) x)

Apply the Product Rule:

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

f = g (h, x), g = x

= h (\frac{d}{d x} (g (h, x)) x + \frac{d x}{d x} g (h, x))

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

= h (\frac{d}{d x} (g (h, x)) x + 1 \cdot g (h, x))

\int_{0}^{2} x e^{4 x} d x

y^{^{'}} = y^{3}, y (0) = 1

\frac{d y}{d t} + \frac{1}{2} y = 17 sin (2 t)

\int cos (2 x) d x

\int (tan (x))^{4} d x

What is the derivative of {g}(h,x(h(x))) ?
The derivative of {g}(h,x(h(x))) is h(derivative of {g}(h,x)x+1*{g}(h,x))
What is the first derivative of {g}(h,x(h(x))) ?
The first derivative of {g}(h,x(h(x))) is h(derivative of {g}(h,x)x+1*{g}(h,x))