What is the derivative of sin(4x+2x^{3/2}) ?

The derivative of sin(4x+2x^{3/2}) is cos(4x)*4+3x^{1/2}

What is the first derivative of sin(4x+2x^{3/2}) ?

The first derivative of sin(4x+2x^{3/2}) is cos(4x)*4+3x^{1/2}

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\frac{d}{d x} (sin (4 x) + 2 x^{\frac{3}{2}})

cos (4 x) \cdot 4 + 3 x^{\frac{1}{2}}

Solution steps

\frac{d}{d x} (sin (4 x) + 2 x^{\frac{3}{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (4 x)) + \frac{d}{d x} (2 x^{\frac{3}{2}})

\frac{d}{d x} (sin (4 x)) = cos (4 x) \cdot 4

\frac{d}{d x} (2 x^{\frac{3}{2}}) = 3 x^{\frac{1}{2}}

= cos (4 x) \cdot 4 + 3 x^{\frac{1}{2}}

sin (x), x = \frac{π}{4}

\frac{d}{d x} ((ln (x)) d x)

x \to - 1 + lim (2 x + 2)

\int e^{x} \cdot cos (\frac{x}{2}) d x

What is the derivative of sin(4x+2x^{3/2}) ?
The derivative of sin(4x+2x^{3/2}) is cos(4x)*4+3x^{1/2}
What is the first derivative of sin(4x+2x^{3/2}) ?
The first derivative of sin(4x+2x^{3/2}) is cos(4x)*4+3x^{1/2}