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

The derivative of (3^{x^2}+x/(2^{x^2)}) is (1+2ln(3)*3^{x^2}x-2ln(2)x(3^{x^2}+x))/(2^{x^2)}

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

The first derivative of (3^{x^2}+x/(2^{x^2)}) is (1+2ln(3)*3^{x^2}x-2ln(2)x(3^{x^2}+x))/(2^{x^2)}

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

\frac{1 + 2 ln ( 3 ) \cdot 3 ^{x^{2}} x - 2 ln ( 2 ) x ( 3 ^{x^{2}} + x )}{2 ^{x^{2}}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

= \frac{( 2 ln ( 3 ) \cdot 3 ^{x^{2}} x + 1 ) \cdot 2 ^{x^{2}} - ln ( 2 ) \cdot 2 ^{x^{2} + 1} x ( 3 ^{x^{2}} + x )}{( 2 ^{x^{2}} ) ^{2}}

Simplify

\frac{( 2 ln ( 3 ) \cdot 3 ^{x^{2}} x + 1 ) \cdot 2 ^{x^{2}} - ln ( 2 ) \cdot 2 ^{x^{2} + 1} x ( 3 ^{x^{2}} + x )}{( 2 ^{x^{2}} ) ^{2}} : \frac{1 + 2 ln ( 3 ) \cdot 3 ^{x^{2}} x - 2 ln ( 2 ) x ( 3 ^{x^{2}} + x )}{2 ^{x^{2}}}

= \frac{1 + 2 ln ( 3 ) \cdot 3 ^{x^{2}} x - 2 ln ( 2 ) x ( 3 ^{x^{2}} + x )}{2 ^{x^{2}}}

\int \frac{2 ( csc ( x ) ) ^{2}}{cot ( x )} d x

\int_{0}^{3} 3 e^{x} d x

\int \frac{6}{( 9 x ^{2} + 1 ) ^{2}} d x

y = \frac{arctan ( 2 x )}{x}

x \to 0 lim ((x + 1)^{l n (x)})

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