What is the derivative of x^5e^{xy}+3x ?

The derivative of x^5e^{xy}+3x is 5x^4e^{xy}+e^{xy}(y+x(dy)/(dx))x^5+3

What is the first derivative of x^5e^{xy}+3x ?

The first derivative of x^5e^{xy}+3x is 5x^4e^{xy}+e^{xy}(y+x(dy)/(dx))x^5+3

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

5 x^{4} e^{x y} + e^{x y} (y + x \frac{d y}{d x}) x^{5} + 3

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (x^{5} e^{x y}) = 5 x^{4} e^{x y} + e^{x y} (y + x \frac{d y}{d x}) x^{5}

\frac{d}{d x} (3 x) = 3

= 5 x^{4} e^{x y} + e^{x y} (y + x \frac{d y}{d x}) x^{5} + 3

f (x) = tan (5 x)

∣ 3 x ∣, x^{2} - 4

ln (\frac{( x - 3 )}{x - 1})

\int_{1}^{4} \frac{4}{x} d x

\int t^{3} cos (t^{2}) d t

What is the derivative of x^5e^{xy}+3x ?
The derivative of x^5e^{xy}+3x is 5x^4e^{xy}+e^{xy}(y+x(dy)/(dx))x^5+3
What is the first derivative of x^5e^{xy}+3x ?
The first derivative of x^5e^{xy}+3x is 5x^4e^{xy}+e^{xy}(y+x(dy)/(dx))x^5+3