What is the derivative of {g}(x(x)^2) ?

The derivative of {g}(x(x)^2) is derivative of {g}(x)x^2+2x{g}(x)

What is the first derivative of {g}(x(x)^2) ?

The first derivative of {g}(x(x)^2) is derivative of {g}(x)x^2+2x{g}(x)

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

\frac{d}{d x} (g (x)) x^{2} + 2 x g (x)

Solution steps

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

Apply the Product Rule:

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

f = g (x), g = x^{2}

= \frac{d}{d x} (g (x)) x^{2} + \frac{d}{d x} (x^{2}) g (x)

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

= \frac{d}{d x} (g (x)) x^{2} + 2 x g (x)

y = 2 sin (x), at x = \frac{3}{4} π

h (x) = \frac{3 x ^{3} - 3}{ln ( x )}

f (x) = 1 - 2 x + x^{2}

f (T) = T

What is the derivative of {g}(x(x)^2) ?
The derivative of {g}(x(x)^2) is derivative of {g}(x)x^2+2x{g}(x)
What is the first derivative of {g}(x(x)^2) ?
The first derivative of {g}(x(x)^2) is derivative of {g}(x)x^2+2x{g}(x)