What is (\partial)/(\partial x)(arctan(7xsqrt(t))) ?

The answer to (\partial)/(\partial x)(arctan(7xsqrt(t))) is (7sqrt(t))/(49x^2t+1)

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(\partial)/(\partial x)(arctan(7xsqrt(t)))

\frac{\partial}{\partial x} (arctan (7 x t))

\frac{7 t}{49 x ^{2} t + 1}

Solution steps

\frac{\partial}{\partial x} (arctan (7 x t))

Treat

t

as a constant

Apply the chain rule:

\frac{1}{( 7 x t ) ^{2} + 1} \frac{\partial}{\partial x} (7 x t)

= \frac{1}{( 7 x t ) ^{2} + 1} \frac{\partial}{\partial x} (7 x t)

\frac{\partial}{\partial x} (7 x t) = 7 t

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

Simplify

\frac{1}{( 7 x t ) ^{2} + 1} \cdot 7 t : \frac{7 t}{49 x ^{2} t + 1}

= \frac{7 t}{49 x ^{2} t + 1}

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What is (\partial)/(\partial x)(arctan(7xsqrt(t))) ?
The answer to (\partial)/(\partial x)(arctan(7xsqrt(t))) is (7sqrt(t))/(49x^2t+1)