What is the derivative of (t^2+5)^2-7(t^2+5) ?

The derivative of (t^2+5)^2-7(t^2+5) is 4t^3+6t

What is the first derivative of (t^2+5)^2-7(t^2+5) ?

The first derivative of (t^2+5)^2-7(t^2+5) is 4t^3+6t

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derivative of

(t^{2} + 5)^{2} - 7 (t^{2} + 5)

4 t^{3} + 6 t

Solution steps

\frac{d}{d t} ((t^{2} + 5)^{2} - 7 (t^{2} + 5))

Simplify

(t^{2} + 5)^{2} - 7 (t^{2} + 5) : t^{4} + 3 t^{2} - 10

= \frac{d}{d t} (t^{4} + 3 t^{2} - 10)

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (t^{4}) + \frac{d}{d t} (3 t^{2}) - \frac{d}{d t} (10)

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

\frac{d}{d t} (3 t^{2}) = 6 t

\frac{d}{d t} (10) = 0

= 4 t^{3} + 6 t - 0

Simplify

= 4 t^{3} + 6 t

What is the derivative of (t^2+5)^2-7(t^2+5) ?
The derivative of (t^2+5)^2-7(t^2+5) is 4t^3+6t
What is the first derivative of (t^2+5)^2-7(t^2+5) ?
The first derivative of (t^2+5)^2-7(t^2+5) is 4t^3+6t