What is the derivative of f(x)=e^{4-5x}(3x^3-2)^6 ?

The derivative of f(x)=e^{4-5x}(3x^3-2)^6 is -5e^{4-5x}(3x^3-2)^6+54e^{4-5x}x^2(3x^3-2)^5

What is the first derivative of f(x)=e^{4-5x}(3x^3-2)^6 ?

The first derivative of f(x)=e^{4-5x}(3x^3-2)^6 is -5e^{4-5x}(3x^3-2)^6+54e^{4-5x}x^2(3x^3-2)^5

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derivative of

f (x) = e^{4 - 5 x} (3 x^{3} - 2)^{6}

- 5 e^{4 - 5 x} (3 x^{3} - 2)^{6} + 54 e^{4 - 5 x} x^{2} (3 x^{3} - 2)^{5}

Solution steps

\frac{d}{d x} (e^{4 - 5 x} (3 x^{3} - 2)^{6})

Apply the Product Rule:

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

f = e^{4 - 5 x}, g = (3 x^{3} - 2)^{6}

= \frac{d}{d x} (e^{4 - 5 x}) (3 x^{3} - 2)^{6} + \frac{d}{d x} ((3 x^{3} - 2)^{6}) e^{4 - 5 x}

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

\frac{d}{d x} ((3 x^{3} - 2)^{6}) = 54 x^{2} (3 x^{3} - 2)^{5}

= (- 5 e^{4 - 5 x}) (3 x^{3} - 2)^{6} + 54 x^{2} (3 x^{3} - 2)^{5} e^{4 - 5 x}

Simplify

= - 5 e^{4 - 5 x} (3 x^{3} - 2)^{6} + 54 e^{4 - 5 x} x^{2} (3 x^{3} - 2)^{5}

y^{^{'}} = 2 x + y, y (0) = 9

y^{^{''}} - y = 10 sin^{2} (x)

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

\int \frac{1}{x ^{2} + 100} d x

n = 0 \sum \infty (\frac{1}{10})^{n}

What is the derivative of f(x)=e^{4-5x}(3x^3-2)^6 ?
The derivative of f(x)=e^{4-5x}(3x^3-2)^6 is -5e^{4-5x}(3x^3-2)^6+54e^{4-5x}x^2(3x^3-2)^5
What is the first derivative of f(x)=e^{4-5x}(3x^3-2)^6 ?
The first derivative of f(x)=e^{4-5x}(3x^3-2)^6 is -5e^{4-5x}(3x^3-2)^6+54e^{4-5x}x^2(3x^3-2)^5