What is (\partial)/(\partial x)(x^2+x/t+sin(x)) ?

The answer to (\partial)/(\partial x)(x^2+x/t+sin(x)) is 2x+1/t+cos(x)

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(\partial)/(\partial x)(x^2+x/t+sin(x))

\frac{\partial}{\partial x} (x^{2} + \frac{x}{t} + sin (x))

2 x + \frac{1}{t} + cos (x)

Solution steps

\frac{\partial}{\partial x} (x^{2} + \frac{x}{t} + sin (x))

Treat

t

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (\frac{x}{t}) + \frac{\partial}{\partial x} (sin (x))

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (\frac{x}{t}) = \frac{1}{t}

\frac{\partial}{\partial x} (sin (x)) = cos (x)

= 2 x + \frac{1}{t} + cos (x)

\frac{d y}{d x} = 18 x^{5} e^{3 x^{6}}

\int (sin (x y)) d y

\frac{d ^{2} x}{d t ^{2}} + 6 \frac{d x}{d t} + 8 x = 5 sin (3 t)

\frac{d ^{2}}{d x ^{2}} (x^{\frac{9}{2}} e^{x})

x \to \infty lim (- 2 (x))

What is (\partial)/(\partial x)(x^2+x/t+sin(x)) ?
The answer to (\partial)/(\partial x)(x^2+x/t+sin(x)) is 2x+1/t+cos(x)