What is (\partial)/(\partial x)(sqrt(3x+4t)) ?

The answer to (\partial)/(\partial x)(sqrt(3x+4t)) is 3/(2sqrt(3x+4t))

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(\partial)/(\partial x)(sqrt(3x+4t))

\frac{\partial}{\partial x} (3 x + 4 t)

\frac{3}{2 3 x + 4 t}

Solution steps

\frac{\partial}{\partial x} (3 x + 4 t)

Treat

t

as a constant

Apply the chain rule:

\frac{1}{2 3 x + 4 t} \frac{\partial}{\partial x} (3 x + 4 t)

= \frac{1}{2 3 x + 4 t} \frac{\partial}{\partial x} (3 x + 4 t)

\frac{\partial}{\partial x} (3 x + 4 t) = 3

= \frac{1}{2 3 x + 4 t} \cdot 3

Simplify

\frac{1}{2 3 x + 4 t} \cdot 3 : \frac{3}{2 3 x + 4 t}

= \frac{3}{2 3 x + 4 t}

f (x) = sin (3 ln (x))

y = 11 x + 11 x + 11 x

x^{2} + x

(x + 1)^{3} (x - 1)

6 y^{^{''}} - 11 y^{^{'}} + 3 y = 0

What is (\partial)/(\partial x)(sqrt(3x+4t)) ?
The answer to (\partial)/(\partial x)(sqrt(3x+4t)) is 3/(2sqrt(3x+4t))