- log tan x
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01.
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dxd
1) tan x 2) cotx 3) sec? x 4) - cosecʻx
Answers
Answer:
Step-by-step explanation:
How do I differentiate trigonometric functions?
First, you should know the derivatives for the basic trigonometric functions:
\dfrac{d}{dx}\sin(x)=\cos(x)
dx
d
sin(x)=cos(x)start fraction, d, divided by, d, x, end fraction, sine, left parenthesis, x, right parenthesis, equals, cosine, left parenthesis, x, right parenthesis
\dfrac{d}{dx}\cos(x)=-\sin(x)
dx
d
cos(x)=−sin(x)start fraction, d, divided by, d, x, end fraction, cosine, left parenthesis, x, right parenthesis, equals, minus, sine, left parenthesis, x, right parenthesis
\dfrac{d}{dx}\tan(x)=\sec^2(x)=\dfrac{1}{\cos^2(x)}
dx
d
tan(x)=sec
2
(x)=
cos
2
(x)
1
start fraction, d, divided by, d, x, end fraction, tangent, left parenthesis, x, right parenthesis, equals, \sec, squared, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, cosine, squared, left parenthesis, x, right parenthesis, end fraction
\dfrac{d}{dx}\cot(x)=-\csc^2(x)=-\dfrac{1}{\sin^2(x)}
dx
d
cot(x)=−csc
2
(x)=−
sin
2
(x)
1
start fraction, d, divided by, d, x, end fraction, cotangent, left parenthesis, x, right parenthesis, equals, minus, \csc, squared, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, sine, squared, left parenthesis, x, right parenthesis, end fraction
\dfrac{d}{dx}\sec(x)=\sec(x)\tan(x)=\dfrac{\sin(x)}{\cos^2(x)}
dx
d
sec(x)=sec(x)tan(x)=
cos
2
(x)
sin(x)
start fraction, d, divided by, d, x, end fraction, \sec, left parenthesis, x, right parenthesis, equals, \sec, left parenthesis, x, right parenthesis, tangent, left parenthesis, x, right parenthesis, equals, start fraction, sine, left parenthesis, x, right parenthesis, divided by, cosine, squared, left parenthesis, x, right parenthesis, end fraction
\dfrac{d}{dx}\csc(x)=-\csc(x)\cot(x)=-\dfrac{\cos(x)}{\sin^2(x)}
dx
d
csc(x)=−csc(x)cot(x)=−
sin
2
(x)
cos(x)
start fraction, d, divided by, d, x, end fraction, \csc, left parenthesis, x, right parenthesis, equals, minus, \csc, left parenthesis, x, right parenthesis, cotangent, left parenthesis, x, right parenthesis, equals, minus, start fraction, cosine, left parenthesis, x, right parenthesis, divided by, sine, squared, left parenthesis, x, right parenthesis, end fraction
You can actually use the derivatives of sine and cosine (along with the quotient rule) to obtain the derivatives of all the other functions.
Want to learn more about differentiating trigonometric functions? Check out this video about sine and cosine, this video about tangent and cotangent, and this video about secant and cosecant.