What is the derivative of y=4tsqrt(t+7) ?

The derivative of y=4tsqrt(t+7) is (2(3t+14))/(sqrt(t+7))

What is the first derivative of y=4tsqrt(t+7) ?

The first derivative of y=4tsqrt(t+7) is (2(3t+14))/(sqrt(t+7))

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derivative of

y = 4 t t + 7

\frac{2 ( 3 t + 14 )}{t + 7}

Solution steps

\frac{d}{d t} (4 t t + 7)

Take the constant out:

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

= 4 \frac{d}{d t} (t t + 7)

Apply the Product Rule:

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

f = t, g = t + 7

= 4 (\frac{d t}{d t} t + 7 + \frac{d}{d t} (t + 7) t)

\frac{d t}{d t} = 1

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

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

Simplify

4 (1 \cdot t + 7 + \frac{1}{2 t + 7} t) : \frac{2 ( 3 t + 14 )}{t + 7}

= \frac{2 ( 3 t + 14 )}{t + 7}

\int_{- 2}^{2} x^{2} - 1 d x

f (x) = 2 e^{- x}

\int 4 sin^{4} (x) cos^{2} (x) d x

\frac{1}{2 + 5 x}

\frac{d y}{d x} = y^{2} - 9

What is the derivative of y=4tsqrt(t+7) ?
The derivative of y=4tsqrt(t+7) is (2(3t+14))/(sqrt(t+7))
What is the first derivative of y=4tsqrt(t+7) ?
The first derivative of y=4tsqrt(t+7) is (2(3t+14))/(sqrt(t+7))