What is the derivative of f(t)=t^6sin(t) ?

The derivative of f(t)=t^6sin(t) is 6t^5sin(t)+cos(t)t^6

What is the first derivative of f(t)=t^6sin(t) ?

The first derivative of f(t)=t^6sin(t) is 6t^5sin(t)+cos(t)t^6

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derivative of

f (t) = t^{6} sin (t)

6 t^{5} sin (t) + cos (t) t^{6}

Solution steps

\frac{d}{d t} (t^{6} sin (t))

Apply the Product Rule:

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

f = t^{6}, g = sin (t)

= \frac{d}{d t} (t^{6}) sin (t) + \frac{d}{d t} (sin (t)) t^{6}

\frac{d}{d t} (t^{6}) = 6 t^{5}

\frac{d}{d t} (sin (t)) = cos (t)

= 6 t^{5} sin (t) + cos (t) t^{6}

cos (- x)

\frac{\partial}{\partial y} (5 x + 4 y)

\int 2 x e^{3 x^{2}} d x

x \to + (- 1) lim (x - 1)

\int_{0}^{2} π (\frac{4}{x ^{2} + 4})^{2} d x

What is the derivative of f(t)=t^6sin(t) ?
The derivative of f(t)=t^6sin(t) is 6t^5sin(t)+cos(t)t^6
What is the first derivative of f(t)=t^6sin(t) ?
The first derivative of f(t)=t^6sin(t) is 6t^5sin(t)+cos(t)t^6