What is the derivative of h(t)=(t^{2/5}+3)(3t^5+5) ?

The derivative of h(t)=(t^{2/5}+3)(3t^5+5) is (81t^5+225t^{23/5}+10)/(5t^{3/5)}

What is the first derivative of h(t)=(t^{2/5}+3)(3t^5+5) ?

The first derivative of h(t)=(t^{2/5}+3)(3t^5+5) is (81t^5+225t^{23/5}+10)/(5t^{3/5)}

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derivative of

h (t) = (t^{\frac{2}{5}} + 3) (3 t^{5} + 5)

\frac{81 t ^{5} + 225 t ^{\frac{23}{5}} + 10}{5 t ^{\frac{3}{5}}}

Solution steps

\frac{d}{d t} ((t^{\frac{2}{5}} + 3) (3 t^{5} + 5))

Apply the Product Rule:

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

f = t^{\frac{2}{5}} + 3, g = 3 t^{5} + 5

= \frac{d}{d t} (t^{\frac{2}{5}} + 3) (3 t^{5} + 5) + \frac{d}{d t} (3 t^{5} + 5) (t^{\frac{2}{5}} + 3)

\frac{d}{d t} (t^{\frac{2}{5}} + 3) = \frac{2}{5 t ^{\frac{3}{5}}}

\frac{d}{d t} (3 t^{5} + 5) = 15 t^{4}

= \frac{2}{5 t ^{\frac{3}{5}}} (3 t^{5} + 5) + 15 t^{4} (t^{\frac{2}{5}} + 3)

Simplify

\frac{2}{5 t ^{\frac{3}{5}}} (3 t^{5} + 5) + 15 t^{4} (t^{\frac{2}{5}} + 3) : \frac{81 t ^{5} + 225 t ^{\frac{23}{5}} + 10}{5 t ^{\frac{3}{5}}}

= \frac{81 t ^{5} + 225 t ^{\frac{23}{5}} + 10}{5 t ^{\frac{3}{5}}}

x \to + 8 - lim (\frac{x}{x - 8})

\frac{d}{d x} (\frac{3 x}{x ^{2} + x})

f (x) = \frac{3}{x}, (1, 3)

y \to 0 lim (\frac{8}{y ^{2} + y} - \frac{8}{y})

y^{^{''}} + 3 y^{^{'}} - 10 y = x (e^{x} + 1)

What is the derivative of h(t)=(t^{2/5}+3)(3t^5+5) ?
The derivative of h(t)=(t^{2/5}+3)(3t^5+5) is (81t^5+225t^{23/5}+10)/(5t^{3/5)}
What is the first derivative of h(t)=(t^{2/5}+3)(3t^5+5) ?
The first derivative of h(t)=(t^{2/5}+3)(3t^5+5) is (81t^5+225t^{23/5}+10)/(5t^{3/5)}