What is the derivative of x=6.4sin(1.2^2t^2) ?

The derivative of x=6.4sin(1.2^2t^2) is 18.432tcos(1.44t^2)

What is the first derivative of x=6.4sin(1.2^2t^2) ?

The first derivative of x=6.4sin(1.2^2t^2) is 18.432tcos(1.44t^2)

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derivative of

x = 6.4 sin (1. 2^{2} t^{2})

18.432 t cos (1.44 t^{2})

Solution steps

\frac{d}{d t} (6.4 sin (1. 2^{2} t^{2}))

Simplify

6.4 sin (1. 2^{2} t^{2}) : 6.4 sin (1.44 t^{2})

= \frac{d}{d t} (6.4 sin (1.44 t^{2}))

Take the constant out:

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

= 6.4 \frac{d}{d t} (sin (1.44 t^{2}))

Apply the chain rule:

cos (1.44 t^{2}) \frac{d}{d t} (1.44 t^{2})

= cos (1.44 t^{2}) \frac{d}{d t} (1.44 t^{2})

\frac{d}{d t} (1.44 t^{2}) = 2.88 t

= 6.4 cos (1.44 t^{2}) \cdot 2.88 t

Simplify

= 18.432 t cos (1.44 t^{2})

What is the derivative of x=6.4sin(1.2^2t^2) ?
The derivative of x=6.4sin(1.2^2t^2) is 18.432tcos(1.44t^2)
What is the first derivative of x=6.4sin(1.2^2t^2) ?
The first derivative of x=6.4sin(1.2^2t^2) is 18.432tcos(1.44t^2)