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

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

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

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

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\frac{d}{d x} (tan (g (x)) x)

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

Solution steps

\frac{d}{d x} (tan (g (x)) x)

Apply the Product Rule:

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

f = tan (g (x)), g = x

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

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

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

= sec^{2} (g (x)) \frac{d}{d x} (g (x)) x + 1 \cdot tan (g (x))

Simplify

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

x \to 0 - lim (x)

\frac{d y}{d x} = - y - 3

y = 6 x^{2}, y^{2} = \frac{1}{6} x

y^{^{''}} + 4 y = - 4 sin (2 t)

\int \frac{2 x}{x ^{2} + 4} d x

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