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

The derivative of 5^{sin(2x)} is 2ln(5)*5^{sin(2x)}cos(2x)

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

The first derivative of 5^{sin(2x)} is 2ln(5)*5^{sin(2x)}cos(2x)

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derivative of

5^{s i n (2 x)}

2 ln (5) \cdot 5^{s i n (2 x)} cos (2 x)

Solution steps

\frac{d}{d x} (5^{s i n (2 x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

5^{s i n (2 x)} = e^{s i n (2 x) l n (5)}

= \frac{d}{d x} (e^{s i n (2 x) l n (5)})

Apply the chain rule:

e^{s i n (2 x) l n (5)} \frac{d}{d x} (sin (2 x) ln (5))

= e^{s i n (2 x) l n (5)} \frac{d}{d x} (sin (2 x) ln (5))

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

= e^{s i n (2 x) l n (5)} ln (5) cos (2 x) \cdot 2

e^{s i n (2 x) l n (5)} = 5^{s i n (2 x)}

= 2 ln (5) \cdot 5^{s i n (2 x)} cos (2 x)

\frac{d y}{d x} = \frac{( x + x y )}{( y + x y )}

\int 5 cos (x) d x

x^{2} + 2 y^{2} = x y y^{^{'}}

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

y = e^{7 x} + 7 x e^{7 x}

What is the derivative of 5^{sin(2x)} ?
The derivative of 5^{sin(2x)} is 2ln(5)*5^{sin(2x)}cos(2x)
What is the first derivative of 5^{sin(2x)} ?
The first derivative of 5^{sin(2x)} is 2ln(5)*5^{sin(2x)}cos(2x)