What is the derivative of 5^{sin(3x}) ?

The derivative of 5^{sin(3x}) is 3ln(5)*5^{sin(3x)}cos(3x)

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

The first derivative of 5^{sin(3x}) is 3ln(5)*5^{sin(3x)}cos(3x)

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\frac{d}{d x} (5^{s i n (3 x)})

3 ln (5) \cdot 5^{s i n (3 x)} cos (3 x)

Solution steps

\frac{d}{d x} (5^{s i n (3 x)})

Apply exponent rule:

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

5^{s i n (3 x)} = e^{s i n (3 x) l n (5)}

= \frac{d}{d x} (e^{s i n (3 x) l n (5)})

Apply the chain rule:

e^{s i n (3 x) l n (5)} \frac{d}{d x} (sin (3 x) ln (5))

= e^{s i n (3 x) l n (5)} \frac{d}{d x} (sin (3 x) ln (5))

\frac{d}{d x} (sin (3 x) ln (5)) = ln (5) cos (3 x) \cdot 3

= e^{s i n (3 x) l n (5)} ln (5) cos (3 x) \cdot 3

e^{s i n (3 x) l n (5)} = 5^{s i n (3 x)}

= 3 ln (5) \cdot 5^{s i n (3 x)} cos (3 x)

x ln (\frac{x}{y}) d y - y d x = 0

\frac{d}{d x} (\frac{6 x ^{2} + 2 x + 4}{x})

f (x) = 6 x e^{x}

\frac{d}{d x} ((x^{4} - 1) (x^{2} + 1))

\int (8 x^{5} - 8 x^{- 3}) d x

What is the derivative of 5^{sin(3x}) ?
The derivative of 5^{sin(3x}) is 3ln(5)*5^{sin(3x)}cos(3x)
What is the first derivative of 5^{sin(3x}) ?
The first derivative of 5^{sin(3x}) is 3ln(5)*5^{sin(3x)}cos(3x)