What is the derivative of 5sin(y+3e^{2x}) ?

The derivative of 5sin(y+3e^{2x}) is cos(y)(dy)/(dx)+6e^{2x}

What is the first derivative of 5sin(y+3e^{2x}) ?

The first derivative of 5sin(y+3e^{2x}) is cos(y)(dy)/(dx)+6e^{2x}

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\frac{d}{d x} (5 sin (y) + 3 e^{2 x})

cos (y) \frac{d y}{d x} + 6 e^{2 x}

Solution steps

\frac{d}{d x} (5 sin (y) + 3 e^{2 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 sin (y)) + \frac{d}{d x} (3 e^{2 x})

\frac{d}{d x} (5 sin (y)) = cos (y) \frac{d y}{d x}

\frac{d}{d x} (3 e^{2 x}) = 6 e^{2 x}

= cos (y) \frac{d y}{d x} + 6 e^{2 x}

y^{^{'}} = \frac{x ^{2} + 3 y ^{2}}{2 x y}

t^{3} - 27 t

\int \frac{x ^{2} + 16 x - 16}{x ^{3} - 16 x} d x

\int \frac{x ^{3}}{8 - x ^{4}} d x

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

What is the derivative of 5sin(y+3e^{2x}) ?
The derivative of 5sin(y+3e^{2x}) is cos(y)(dy)/(dx)+6e^{2x}
What is the first derivative of 5sin(y+3e^{2x}) ?
The first derivative of 5sin(y+3e^{2x}) is cos(y)(dy)/(dx)+6e^{2x}