What is the derivative of tan(5sqrt(x)) ?

The derivative of tan(5sqrt(x)) is (5sec^2(5sqrt(x)))/(2sqrt(x))

What is the first derivative of tan(5sqrt(x)) ?

The first derivative of tan(5sqrt(x)) is (5sec^2(5sqrt(x)))/(2sqrt(x))

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derivative of

tan (5 x)

\frac{5 sec ^{2} ( 5 x )}{2 x}

Solution steps

\frac{d}{d x} (tan (5 x))

Apply the chain rule:

sec^{2} (5 x) \frac{d}{d x} (5 x)

= sec^{2} (5 x) \frac{d}{d x} (5 x)

\frac{d}{d x} (5 x) = \frac{5}{2 x}

= sec^{2} (5 x) \frac{5}{2 x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 sec ^{2} ( 5 x )}{2 x}

\int \frac{cos ( 4 x )}{2} d x

\int sec (x) tan (x) (\frac{x}{π}) d x

\frac{d y}{d t} + y = cos (2 t), y (0) = 5

\frac{d y}{d x} = \frac{1}{x y}

f (x) = x x^{3} - 6

What is the derivative of tan(5sqrt(x)) ?
The derivative of tan(5sqrt(x)) is (5sec^2(5sqrt(x)))/(2sqrt(x))
What is the first derivative of tan(5sqrt(x)) ?
The first derivative of tan(5sqrt(x)) is (5sec^2(5sqrt(x)))/(2sqrt(x))