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Popular >

derivative of sqrt(t+t^3)

Solution

derivative of

t + t^{3}

Solution

\frac{1 + 3 t ^{2}}{2 t + t ^{3}}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 t + t ^{3}} (1 + 3 t^{2})

Simplify

\frac{1}{2 t + t ^{3}} (1 + 3 t^{2}) : \frac{1 + 3 t ^{2}}{2 t + t ^{3}}

= \frac{1 + 3 t ^{2}}{2 t + t ^{3}}

Popular Examples

\frac{d y}{d x} = 8 - 4 y

integral of (e^{2sqrt(x)})/(3sqrt(x))

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

derivative of x^3-4x+7

\frac{d}{d x} (x^{3} - 4 x + 7)

limit as x approaches 1 of x^2+x-2

x \to 1 lim (x^{2} + x - 2)

d/(d{x)}(sqrt({x)^2+{y}^2+{z}^2})

\frac{d}{d x} (x^{2} + y^{2} + z^{2})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(t+t^3) ?
The derivative of sqrt(t+t^3) is (1+3t^2)/(2sqrt(t+t^3))
What is the first derivative of sqrt(t+t^3) ?
The first derivative of sqrt(t+t^3) is (1+3t^2)/(2sqrt(t+t^3))