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Popular >

derivative of 4(t)+|4(t)-1|

Solution

derivative of

4 (t) + ∣ 4 (t) - 1 ∣

Solution

4 + \frac{4 ( 4 t - 1 )}{∣ 4 t - 1 ∣}

Solution steps

\frac{d}{d t} (4 t + ∣ 4 t - 1 ∣)

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (4 t) + \frac{d}{d t} (∣ 4 t - 1 ∣)

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

\frac{d}{d t} (∣ 4 t - 1 ∣) = \frac{4 ( 4 t - 1 )}{∣ 4 t - 1 ∣}

= 4 + \frac{4 ( 4 t - 1 )}{∣ 4 t - 1 ∣}

Popular Examples

integral of 1/((x^2-6x+13)^2)

\int \frac{1}{( x ^{2} - 6 x + 13 ) ^{2}} d x

integral from 0 to 1 of (50)/(4y-1)

\int_{0}^{1} \frac{50}{4 y - 1} d y

laplacetransform {t+e^{2t}}laplace transform

{t + e^{2 t}}

x*(y^2-1)=y*(4-x^2)*y^'

x \cdot (y^{2} - 1) = y \cdot (4 - x^{2}) \cdot y^{^{'}}

(\partial)/(\partial y)(y^2e^{-2x})

\frac{\partial}{\partial y} (y^{2} e^{- 2 x})

Frequently Asked Questions (FAQ)

What is the derivative of 4(t)+|4(t)-1| ?
The derivative of 4(t)+|4(t)-1| is 4+(4(4t-1))/(|4t-1|)
What is the first derivative of 4(t)+|4(t)-1| ?
The first derivative of 4(t)+|4(t)-1| is 4+(4(4t-1))/(|4t-1|)