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Popular >

derivative of (3sin(x+sqrt(x))^3)

Solution

\frac{d}{d x} ((3 sin (x) + x)^{3})

Solution

3 (3 sin (x) + x)^{2} (3 cos (x) + \frac{1}{2 x})

Solution steps

\frac{d}{d x} ((3 sin (x) + x)^{3})

Apply the chain rule:

3 (3 sin (x) + x)^{2} \frac{d}{d x} (3 sin (x) + x)

= 3 (3 sin (x) + x)^{2} \frac{d}{d x} (3 sin (x) + x)

\frac{d}{d x} (3 sin (x) + x) = 3 cos (x) + \frac{1}{2 x}

= 3 (3 sin (x) + x)^{2} (3 cos (x) + \frac{1}{2 x})

Graph

Popular Examples

limit as x approaches 2 of (3-sqrt(4x+1))/((x^2-2x))

x \to 2 lim (\frac{3 - 4 x + 1}{( x ^{2} - 2 x )})

laplacetransform sin(t+(11pi)/2)laplace transform

sin (t + \frac{11 π}{2})

limit as x approaches 1 of (3x)/(2x+2)

x \to 1 lim (\frac{3 x}{2 x + 2})

y^'=(6x^5y)/(ln(y))

y^{^{'}} = \frac{6 x ^{5} y}{ln ( y )}

y^{''}+6y^'-7y=0

y^{^{''}} + 6 y^{^{'}} - 7 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of (3sin(x+sqrt(x))^3) ?
The derivative of (3sin(x+sqrt(x))^3) is 3(3sin(x)+sqrt(x))^2(3cos(x)+1/(2sqrt(x)))
What is the first derivative of (3sin(x+sqrt(x))^3) ?
The first derivative of (3sin(x+sqrt(x))^3) is 3(3sin(x)+sqrt(x))^2(3cos(x)+1/(2sqrt(x)))