What is the derivative of 5^{x^2}ln(tan(x)) ?

The derivative of 5^{x^2}ln(tan(x)) is 2ln(5)*5^{x^2}xln(tan(x))+2csc(2x)*5^{x^2}

What is the first derivative of 5^{x^2}ln(tan(x)) ?

The first derivative of 5^{x^2}ln(tan(x)) is 2ln(5)*5^{x^2}xln(tan(x))+2csc(2x)*5^{x^2}

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\frac{d}{d x} (5^{x^{2}} ln (tan (x)))

2 ln (5) \cdot 5^{x^{2}} x ln (tan (x)) + 2 csc (2 x) \cdot 5^{x^{2}}

Solution steps

\frac{d}{d x} (5^{x^{2}} ln (tan (x)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 5^{x^{2}}, g = ln (tan (x))

= \frac{d}{d x} (5^{x^{2}}) ln (tan (x)) + \frac{d}{d x} (ln (tan (x))) 5^{x^{2}}

\frac{d}{d x} (5^{x^{2}}) = 2 ln (5) \cdot 5^{x^{2}} x

\frac{d}{d x} (ln (tan (x))) = 2 csc (2 x)

= 2 ln (5) \cdot 5^{x^{2}} x ln (tan (x)) + 2 csc (2 x) \cdot 5^{x^{2}}

\int x sin (x) + 1 d x

\int \frac{ln ( t )}{t ^{6}} d t

\int_{2}^{4} (x - 2) d x

\int (\frac{3 + 5 x - 6 x ^{2} - 7 x ^{3}}{2 x ^{2}}) d x

f (x) = x^{2} - 5 x + 5, at x = 4

What is the derivative of 5^{x^2}ln(tan(x)) ?
The derivative of 5^{x^2}ln(tan(x)) is 2ln(5)*5^{x^2}xln(tan(x))+2csc(2x)*5^{x^2}
What is the first derivative of 5^{x^2}ln(tan(x)) ?
The first derivative of 5^{x^2}ln(tan(x)) is 2ln(5)*5^{x^2}xln(tan(x))+2csc(2x)*5^{x^2}