What is the derivative of (3t^5-1)/(x^2+2) ?

The derivative of (3t^5-1)/(x^2+2) is (15t^4)/(x^2+2)

What is the first derivative of (3t^5-1)/(x^2+2) ?

The first derivative of (3t^5-1)/(x^2+2) is (15t^4)/(x^2+2)

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derivative of

\frac{3 t ^{5} - 1}{x ^{2} + 2}

\frac{15 t ^{4}}{x ^{2} + 2}

Solution steps

\frac{d}{d t} (\frac{3 t ^{5} - 1}{x ^{2} + 2})

Treat

x

as a constant

Take the constant out:

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

= \frac{1}{x ^{2} + 2} \frac{d}{d t} (3 t^{5} - 1)

Apply the Sum/Difference Rule:

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

= \frac{1}{x ^{2} + 2} (\frac{d}{d t} (3 t^{5}) - \frac{d}{d t} (1))

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

\frac{d}{d t} (1) = 0

= \frac{1}{x ^{2} + 2} (15 t^{4} - 0)

Simplify

\frac{1}{x ^{2} + 2} (15 t^{4} - 0) : \frac{15 t ^{4}}{x ^{2} + 2}

= \frac{15 t ^{4}}{x ^{2} + 2}

What is the derivative of (3t^5-1)/(x^2+2) ?
The derivative of (3t^5-1)/(x^2+2) is (15t^4)/(x^2+2)
What is the first derivative of (3t^5-1)/(x^2+2) ?
The first derivative of (3t^5-1)/(x^2+2) is (15t^4)/(x^2+2)