en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(t)=(1+sqrt(t))(2t^2-7)

Solution

derivative of

f (t) = (1 + t) (2 t^{2} - 7)

Solution

\frac{10 t ^{2} + 8 t t - 7}{2 t}

Solution steps

\frac{d}{d t} ((1 + t) (2 t^{2} - 7))

Apply the Product Rule:

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

f = 1 + t, g = 2 t^{2} - 7

= \frac{d}{d t} (1 + t) (2 t^{2} - 7) + \frac{d}{d t} (2 t^{2} - 7) (1 + t)

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

\frac{d}{d t} (2 t^{2} - 7) = 4 t

= \frac{1}{2 t} (2 t^{2} - 7) + 4 t (1 + t)

Simplify

\frac{1}{2 t} (2 t^{2} - 7) + 4 t (1 + t) : \frac{10 t ^{2} + 8 t t - 7}{2 t}

= \frac{10 t ^{2} + 8 t t - 7}{2 t}

Popular Examples

integral of x^1((5x^2+2/3)^4)/1

\int x^{1} \frac{( 5 x ^{2} + \frac{2}{3} ) ^{4}}{1} d x

d/(dt)((d/(dt)(e^tcos(t)))^2)

\frac{d}{d t} ((\frac{d}{d t} (e^{t} cos (t)))^{2})

derivative of f(x)=(e^{x^2})/(x^3)derivative of

f (x) = \frac{e ^{x^{2}}}{x ^{3}}

limit as x approaches 0 of xln(1-2/(3w(x)))

x \to 0 lim (x ln (1 - \frac{2}{3 w ( x )}))

limit as x approaches-3 of 2x^2-3x+4

x \to - 3 lim (2 x^{2} - 3 x + 4)

Frequently Asked Questions (FAQ)

What is the derivative of f(t)=(1+sqrt(t))(2t^2-7) ?
The derivative of f(t)=(1+sqrt(t))(2t^2-7) is (10t^2+8tsqrt(t)-7)/(2sqrt(t))
What is the first derivative of f(t)=(1+sqrt(t))(2t^2-7) ?
The first derivative of f(t)=(1+sqrt(t))(2t^2-7) is (10t^2+8tsqrt(t)-7)/(2sqrt(t))