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Popular >

derivative of 27arctan(sqrt(x))

Solution

\frac{d}{d x} (27 arctan (x))

Solution

\frac{27}{2 x ( x + 1 )}

Solution steps

\frac{d}{d x} (27 arctan (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 27 \frac{d}{d x} (arctan (x))

Apply the chain rule:

\frac{1}{( x ) ^{2} + 1} \frac{d}{d x} (x)

= \frac{1}{( x ) ^{2} + 1} \frac{d}{d x} (x)

\frac{d}{d x} (x) = \frac{1}{2 x}

= 27 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x}

Simplify

27 \cdot \frac{1}{( x ) ^{2} + 1} \cdot \frac{1}{2 x} : \frac{27}{2 x ( x + 1 )}

= \frac{27}{2 x ( x + 1 )}

Popular Examples

(\partial)/(\partial x)(x^2+xy+3x+2y+5)

\frac{\partial}{\partial x} (x^{2} + x y + 3 x + 2 y + 5)

y^{''}+4y^'+4y=-3e^{2t},y(0)=1,y^'(0)=0

y^{^{''}} + 4 y^{^{'}} + 4 y = - 3 e^{2 t}, y (0) = 1, y^{^{'}} (0) = 0

(\partial)/(\partial x)(x^2+y^2-1)

\frac{\partial}{\partial x} (x^{2} + y^{2} - 1)

derivative of f(x)=x^3-7x^2-7x+4 derivative of

f (x) = x^{3} - 7 x^{2} - 7 x + 4

laplacetransform-9t laplace transform

- 9 t

Frequently Asked Questions (FAQ)

What is the derivative of 27arctan(sqrt(x)) ?
The derivative of 27arctan(sqrt(x)) is (27)/(2sqrt(x)(x+1))
What is the first derivative of 27arctan(sqrt(x)) ?
The first derivative of 27arctan(sqrt(x)) is (27)/(2sqrt(x)(x+1))