Calculate the derivatives of all orders: f'(x),f''(x),f'''(x),f^{4}(x),...f^{n}(x),...f(x)=e^{2x}

Tahmid Knox

Tahmid Knox

Answered question

2021-06-27

Calculate the derivatives of all orders:
f(x),f(x),f(x),f4(x),fn(x),f(x)=e2x

Answer & Explanation

un4t5o4v

un4t5o4v

Skilled2021-06-28Added 105 answers

f(x)=e2x Find f'(x), differentiate both sides with respect to x
f(x)=ddx[e2x]
f(x)=2e2x
Find f''(x)
f(x)=ddx[f(x)]
fx)=ddx[2e2x]
f(x)=4e2x
f(x)=22e2x
Find f'''(x) f(x)=8e2x
f(x)=23e2x
Find f4(x)
f(4)(x)=24e2x
f(4)(x)=16e2x
Therefore,
fn(x)=2ne2x

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