What is (\partial)/(\partial t)(cos(xt)+3tx^2) ?

The answer to (\partial)/(\partial t)(cos(xt)+3tx^2) is -sin(xt)x+3x^2

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(\partial)/(\partial t)(cos(xt)+3tx^2)

\frac{\partial}{\partial t} (cos (x t) + 3 t x^{2})

- sin (x t) x + 3 x^{2}

Solution steps

\frac{\partial}{\partial t} (cos (x t) + 3 t x^{2})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial t} (cos (x t)) + \frac{\partial}{\partial t} (3 t x^{2})

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

\frac{\partial}{\partial t} (3 t x^{2}) = 3 x^{2}

= - sin (x t) x + 3 x^{2}

\int \frac{sin ( x )}{cos ^{2} ( x ) + cos ( x ) - 6} d x

f (x) = x^{2} - 3 x + 5, at x = 1

n = 0 \sum \infty n^{3}

f (x) = - 7 x^{3} - 8 x^{2} - 5 x, at x = - 3

\int \frac{sin ( 2 x )}{1 + cos ( 2 x )} d x

What is (\partial)/(\partial t)(cos(xt)+3tx^2) ?
The answer to (\partial)/(\partial t)(cos(xt)+3tx^2) is -sin(xt)x+3x^2