What is the derivative of (t(x^2+y^2-z(t)^2)) ?

The derivative of (t(x^2+y^2-z(t)^2)) is t(2x+2y derivative of y-t^2 derivative of {z}(t))

What is the first derivative of (t(x^2+y^2-z(t)^2)) ?

The first derivative of (t(x^2+y^2-z(t)^2)) is t(2x+2y derivative of y-t^2 derivative of {z}(t))

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\frac{d}{d x} ((t) (x^{2} + y^{2} - z (t) (t)^{2}))

t (2 x + 2 y \frac{d}{d x} (y) - t^{2} \frac{d}{d x} (z (t)))

Solution steps

\frac{d}{d x} ((t) (x^{2} + y^{2} - z (t) (t)^{2}))

Treat

t

as a constant

Take the constant out:

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

= t \frac{d}{d x} (x^{2} + y^{2} - z (t) t^{2})

Apply the Sum/Difference Rule:

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

= t (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (y^{2}) - \frac{d}{d x} (z (t) t^{2}))

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

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

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

= t (2 x + 2 y \frac{d}{d x} (y) - t^{2} \frac{d}{d x} (z (t)))

(2 (y \cdot v)) (d y \cdot v + y \cdot d v)

\frac{arccosh ( e ^{- x} )}{e ^{- x}}

\frac{1}{( s + 9 ) ( s ^{2} + k ^{2} )}

\frac{x - 1}{( x + 1 ) ^{3}}

(3 x^{2} - 1) d x

What is the derivative of (t(x^2+y^2-z(t)^2)) ?
The derivative of (t(x^2+y^2-z(t)^2)) is t(2x+2y derivative of y-t^2 derivative of {z}(t))
What is the first derivative of (t(x^2+y^2-z(t)^2)) ?
The first derivative of (t(x^2+y^2-z(t)^2)) is t(2x+2y derivative of y-t^2 derivative of {z}(t))